This lecture is part of Maths 1.15 Berkeley, an introductory undergraduate course on number theory, and will be mostly about Dirichlet series. So these are named after Dirichlet, and Dirichlet actually is one of the most impressive names of mathematicians, so his full name looked like this. I'm not quite sure why he had so many names, but his family name was apparently this double-barreled thing, so Dirichlet is really an abbreviation of his name. Anyway, Dirichlet series are a special case of generating functions, so I'll just stop by reviewing the concept of a generating function. So the most common form of an example of a generating function is a generating function that's a power series. So if we've got some sort of series of numbers, c0, c1, c2, we can encode them as a power series, c0 plus c1x plus c2x squared, and so on. So you might write this as a function, then you try and convert properties of the series ci into properties of the function f of x. So I'll just give one example of this, of the Fibonacci numbers. So the Fibonacci numbers are the property that f of n plus 2 is equal to f of n plus 1 plus f of n, and we take f0 equals 0, and f1 equals 1. So the first few numbers go 0, 1, 1, 2, 3, 5, 8, 13, and so on. And the problem is to find an explicit formula for these. So what we do is, you first of all put f of x equal to f0 x to 0 plus f1 x to 1 and so on. Now we try and find this function f of x by turning this recursion relation for the coefficients into some sort of formula for f of x. And if we write this out, we notice that x times f of x is equal to f0 x plus f1 x squared and so on. So f2 x squared. And x squared times f of x is equal to f of 0 plus f1 and so on. And now you notice that the recursion formula shows that if we take 1 minus x minus x squared times big f of x, so we're taking this term minus this term minus this term, then you notice everything cancels out except for these terms here, which just give us the factor of x. So we have this formula here.  So we know f of x is now equal to x over 1 minus x minus x squared, which is equal to x over 1 minus phi of x times 1 minus 1 minus phi of x, where we've just taken phi to be one of the roots of this. So phi is equal to root 5 plus 1 over 2. We can write this as partial fractions. So this becomes 1 over root 5 times 1 over 1 minus phi of x minus 1 over 1 minus 1 minus phi of x, straightforward calculation. And now we can expand both of these as power series, and we see this is equal to 1 over root 5 times sum over all n of x to the n times phi to the n minus 1 minus phi to the n. So we've now got an explicit formula for the Fibonacci numbers. f of n is just 1 over root 5 times phi to the n minus 1 minus phi to the n, if I've got everything right. So that's a typical use of generating functions. The idea is you start with some sequence of numbers, you convert it into a function, you identify what this function is, and then you can work back and find information about your original sequence of numbers. So we try doing this with arithmetical functions. For example, we can take Euler's function phi of n, which is the number of integers less than n coprime to n, and we can try and form a power series. So phi of 1 times x to the 1 plus phi of 2 times x squared plus phi of 3 times x cubed and so on. So this looks like x plus x squared plus 2x cubed and so on. And the problem is this function here just seems to be a complete mess, and it's rather difficult to say anything much about it. For example, phi of n has this multiplicativity property, phi of mn is equal to phi of m times phi of n whenever m and n are coprime. And it's very difficult to convert this multiplicativity property to a nice property of this power series. So this just doesn't seem to work very well. However, power series are not the only form of generating function. What we can do is we can form a Dirichlet series. So if we've got a sequence of numbers c1, c2, c3, then instead of forming the power series with these as coefficients, it often turns out to be a good idea to form the following series. We take c1 over 1 to the s plus c2 over 2 to the s plus c3 over 3 to the s and so on. So you've got this function which is you traditionally use s as the variable for a Dirichlet series. And this sometimes works much better for arithmetical functions. So let's do some a few examples of this. The first example is we just take the series 1, 1, 1, 1 and so on. Now for power series, this doesn't give us anything terribly interesting because 1 plus x plus x squared and so on is just 1 over 1 minus x. So it's a fairly elementary function. For Dirichlet series, what we get is the function 1 over 1 to the s plus 1 over 2 to the s plus 1 over 3 to the s and so on. And this is the notorious Riemann zeta function which has caused more headaches than any other function in mathematics. So let's just review some properties of the Riemann zeta function.  That follows easily by comparison with the integral of 1 over x to the s from 1 to infinity. So this is a decreasing function of x. So the integral converges exactly when the series converges. At s equals 1, it definitely diverges because we get the harmonic series, which is well known for actually being infinite. The other another really useful property of the Riemann zeta function is its infinite product expansion.  So this is a product over all primes p of 1 over 1 minus p to the minus s. And this sort of product expansion turns up a lot when you're studying the Ricollet series. So if we just quickly recall the proof of this, all you do is that you expand 1 over 1 minus 2 to the minus s as being 1 plus 2 to the minus s plus 2 to the minus s squared plus 2 to the minus s cubed and so on.  And you get the same thing for 5 and for all other primes. And now if you multiply these all together, then you take a factor of 1 from most of them, but a factor of, and one of the factors further along. So for example, one of the many factors in the power series expansion, you will take 2 to the minus s cubed times 3 to the minus s and maybe you have a 7 to the minus s. And the product of these three factors and all these ones will be 2 to the minus 3s times 3 to the minus s times 7 to the minus s, which is equal to 2 cubed times 3 times 7 to the minus s. And what you notice is that every integer can be written as a product of powers of primes in a unique, so every positive integer can be written as a product of powers of primes in a unique way by the fundamental theorem of arithmetic, which means that every integer turns up exactly once when you multiply all these together. So this just becomes 1 over 1 to the s plus 1 over 2 to the s and so on. So the infinite product formula for the Riemann-Zeta function is equivalent to the fundamental theorem of arithmetic. So now let's see some other examples of this. First of all, we notice that this thing about having an infinite product expansion works whenever the series is multiplicative, so suppose you've got a series c1 over 1 to the s plus c2 over 2 to the s and so on. And suppose that the ci's are multiplicative, so cmn is equal to cm times cn, never m and n a co-prime. Then you can do this same trick, so this is, so here we have c1 equals 1, so so what we can do is we can multiply out 1 over 1 to the s plus c2 over 2 to the s plus c4 over 2 to the 2s and so on times 1 over 1 to the s plus c3 over 3 to the s plus c9 over 3 to the 2s and so on. And if we multiply this out just as before, we will get a lot of terms that a typical term will look something like, we might have a c4 over 2 to the 2s times c3 over 3 to the s times maybe c5 over 5 to the 2s. And what we will be getting is terms like c2 squared times c3 times c5 5 squared divided by 2 squared to the s times 3 to the s times 5 squared to the s. And this is equal to c2 squared times 3 times 5 squared over 2 squared times 3 times 5 squared to the s because the c's are multiplicative. So these two expressions are equal exactly when the c i's are a multiplicative function. And we can use this to identify a lot of Dirichlet series. So let's have some examples. The first simple example is just n to the k. So this is obviously multiplicative. In fact, it's strictly multiplicative because mn to the k is equal to m to the k times n to the k. And if we look at the corresponding Dirichlet series, we get 1 over 1 to the s plus 2 to the k over 2 to the s plus 3 to the k over 3 to the s. And it's not very difficult to figure out what this is. This is just zeta of s minus k. So I just sort of shifted zeta by a constant. And of course the product formula for zeta gives you a product formula for zeta of k minus s. So that's not terribly interesting. This is equal to product over p 1 over 1 minus p to the k minus s. So now let's go back to Euler's function phi of n. Now we recall this as multiplicative. So in order to work it out, the easiest way is just to find out its Euler product. So what we try and do is we work out 1 over 1 to the s plus 5p over p to the s plus phi of p squared over p to the 2s and so on. So this is called the Euler factor at the prime p. So all we have to do is to work out what this is.   And this splits as a sum of geometric series and you can see what it is.  So sum of phi n times n to the s is equal to a product over all primes of 1 minus p to minus s over 1 minus p to the 1 minus s. And now we can see that this is just the factor we were getting for zeta of s and this is just the factor we were getting for zeta of s minus 1. So this is equal to zeta of s minus 1 over zeta of s. So when we take Euler's phi function as the coefficients of a power series we just get a horrible mess. When we take it as the coefficients of Dirichlet's series we actually get a reasonably nice function out of it. So now let's do the function tau of n which is the number of divisors of n. So tau of 1 is equal to 1, tau of 2 is equal to 2, tau of 3 is equal to 2 because 3 is 2 divisors and tau of 4 is equal to 3 because 4 is 3 divisors 1, 2 and 4 and so on. And we recall that tau of mn is tau of m times tau of n whenever m and n prime. So we can work out the Dirichlet's series tau of 1 over 1 to the s plus tau of 2 to the s and so on by working out the Euler factors and multiplying them together. And now we notice that tau of p to the k is just k plus 1 because the factors are 1 p p squared up to p to the k. So the Euler factor is going to be 1 over 1 to the s plus tau of p over p to the s plus tau of p squared over p to the 2s and so on which is 1 over 1 to the s plus 2 over p to the s plus 3 over p to the 2s and so on. And how do we sum this? Well this is just not quite a geometric series but it's quite close. It's something of the form 1 plus 2x plus 3x squared and so on and you probably recall from calculus that this is just 1 over 1 minus x squared. So this becomes 1 over 1 minus p to the minus s all squared. So this sum here becomes the product over all p of 1 over 1 minus p to the minus s squared which is obviously just zeta of s squared. So now let's look at a slightly more complicated example. Let's look at sigma of n which is the sum of the divisors of n. So sigma 1 is just 1, sigma 2 is 1 plus 2 which is 3, sigma 3 is 1 plus 3 which is 4 and sigma 4 is 1 plus 2 plus 4 which is equal to 7 and so on. So we're going to look at sigma 1 over 1 to the s plus sigma 2 to the s plus sigma 3 over 3 to the s and so on. And just as before we recall that sigma is multiplicative, sigma mn, sigma m times sigma n whenever m and n are co-primed so we just work out the Euler factors. And now we need to know what sigma of p to the k is. Well this is just 1 plus p plus p squared all the way up to plus p to the k which is equal to p to the k plus 1 minus 1 divided by p minus 1.   So if you multiply this out it's just the series 1 plus 1 over p to the s plus 1 over p to the 2s and so on times 1 plus p over p to the s plus p squared over p to the 2s and so on.  So sum of sigma n over n to the s is just the product over all p 1 over 1 minus p to the minus s times 1 minus p to the 1 minus s and this is just zeta of s times zeta of s minus 1. There's something very similar you can do if you if you define sigma k of n to be the sum overall d dividing n of the k's powers of d then we can also form sum of sigma k of n over n to the s and this turns out to be zeta of s times zeta of s minus k. And the proof of this is very similar to the case of sigma n so I'm not going to write it out in detail. We just noticed that sigma 0 of n was just the number of divisors and sigma 1 of n was just the sum of the divisors. So the two special cases of this here we get sigma of s times sigma of s minus 0 and here we get sigma of s times sigma of s minus 1 so the two results about sigma and tau that I gave are special cases of this more general result. Next we come to the Moebius function mu of n and it's defining this rather peculiar way so it's equal to 0 if n is divisible by a square greater than 1 and it's equal to minus 1 to the k if n is a product of k distinct primes. This seems to be a completely bizarre definition but you'll see why it's a useful definition in a moment. So let's just look at a few values of it so if n is equal to 1 2 3 4 5 6 7 8 then mu of n is equal to 1 minus 1 minus 1 0 minus 1 1 minus 1 0 and so on. So it sort of oscillates in a more or less random fashion between 1 and minus 1 except it's sometimes 0 as well. So where on earth does this funny looking function come from? Well the explanation comes if you look at sum of mu to the n over n to the s and now you can see mu is multiplicative so we can write this as a product of its oiler product so let's look at 1 plus mu of p over p to the s plus mu of p squared over p to the 2s and so on well this is incredibly easy to work out because most of these terms just vanish this is just equal to 1 minus 1 over p to the s. So this sum here is just product overall primes of 1 minus p to the minus s and now we see this is just 1 over zeta of s so this sort of explains where this funny definition comes from is just the Dirichlet series coefficients of 1 over zeta of s. Well you may think it would have been more natural to define mu lambda of n to be minus 1 to the number of prime factors of n so it's like mu except it's never zero so if n is equal to 1 2 3 4 5 6 7 8 then lambda of n is well here it's 1 minus 1 minus 1 now it's plus 1 instead of zero for mu of n minus 1 plus 1 minus 1 and now it's going to be minus 1 again so so it's a bit like mu except whenever n is divisible by square it's it's it's not zero and we can work out some of lambda n over n to the s in much the same way so the corresponding Euler factor is 1 plus minus 1 over p to the s plus plus 1 over p to the 2 s and so on which is equal to 1 minus 1 over p to the s plus 1 over p to the 2 s minus and so on this is just a geometric series which is equal to 1 over 1 plus p to the minus s so how do we work this out so we want the product overall primes of 1 over 1 plus p to the minus s well there's a neat trick for doing this we can write this as a product overall primes of 1 minus p to the minus s over 1 minus p to the minus 2 s so and now each of these can be each of these products can be written in terms of the Riemann zeta functions this just becomes zeta of 2 s over zeta of s if I've got it the right way round so we can also look at an example of Dirichlet characters and these will be coming up later so let's just give a very simple example as far as I put chi of n to be given as follows so it's plus 1 if n is congruent to 1 mod 4 minus 1 if n is congruent to 3 mod 4 and 0 if n is even this is about the simplest non-trivial example of a Dirichlet character so so the sum of chi of n over n to the s looked like this it's 1 over 1 to the s minus 1 over 3 to the s plus 1 over 5 to the s minus 1 over 7 to the s and so on and we we can write this as an Euler product as follows so what we need to work out is for each prime p we need to work out 1 over 1 to the s plus chi of p over p to the s and so on plus chi of p squared over p to the 2 s and this obviously depends on what p is modulo 4 so if p equals 2 we just get 1 because all these terms are 0 if p is congruent to 1 mod 4 we get 1 plus 1 over p to the s plus 1 over p to the 2 s and so on which is equal to 1 over 1 minus p to the minus s if p is congruent to 3 mod 4 we get 1 minus 1 over p to the s plus 1 over p to the 2 s and so on which is 1 over 1 plus p to the minus s and in all cases you see that the factor we get is actually 1 over 1 minus chi of p times p to the minus s so this Dirichlet series l of s is just the product over all primes of 1 over 1 minus chi of p times p to the minus s and we'll be seeing lots of examples of this coming up in a few lectures time now let's give an example finished by giving the example that is not multiplicative this is the the function sometimes denoted by lambda of n which has the following rather funny definition it's equal to log of p if n is equal to p to the k for k greater than or equal to 1 and p prime and it's equal to 0 otherwise and it's definitely not multiplicative so we can't write it as an Euler product and you may ask where does this rather bizarre looking function come from well it turns out that um sum of um so lambda 0 over so lambda 1 over 1 to the s plus lambda 2 over 2 to the s plus lambda 3 over 3 to the s and so on turns out to be the zeta prime of s over zeta of s which is actually the the derivative of the log of zeta of s and this this function turns out to be really important when you're trying to count primes because it enables you to turn the problem of counting primes into the problem of studying the Riemann zeta function and to see this it isn't very difficult so we start with zeta of s is the product overall primes of of not taking long yet of 1 over 1 minus p to the minus s so log of zeta of s is sum overall primes of log of 1 minus p to the minus s which is just the sum overall primes of minus sorry p to the minus s plus p to the minus 2s over 2 plus p to the minus 3s over 3 and so on so we we're just writing down the usual power series for log of 1 minus x and now if we differentiate it with respect to s we get the sum overall p of log of p times p to the minus s plus log of p times p to the minus 2s plus log of p times p to the minus 3s and so on and you notice when we differentiate p to the minus 3s we get a factor of 3 but that then cancels out with this 3 in the denominator so this this is a sum over all primes and sum over all n's of log p times p to the minus ns so this is just the sum overall n of lambda n times n to the minus s so this function will be turning up when we briefly discuss the prime number theorem in in in a couple of lectures time okay um so um the next video will be about converting various other properties of um arithmetical functions into properties of Dirichlet series


Going on everyone Sam here with latent sports cards Ribbon 23 penini prison football hobby six-box half-case break number 18 picker team style names and teams Alberto S with the Browns Andrew J Rams Ashley W. Bengals Cody W. Broncos and dolphins Dan M with the Falcons Daniel D. Bills Gou H. Jags James P. Eagles Jamie S with the Lions Jason M. Giants Jeffrey H. Ravens Jonathan G. Texan Jordan W. Cowboys Joseph C. Vikings Josh and Titans Freddie C. with the Panthers Matthew B. Cardinals Michael M. Chiefs Nathan A. Bears Nicholas U. Saints Nicholas O. Colts Philip T. Raiders Patriots Bucks Commanders Robert M. With the Chargers and the Steelers Steven L. With the Niners and Seahawks Steve B. Jets and V-POTC with the Packers So good luck here everybody. Let's do it Jason picking up the Browns in the next one down to nine already Single digits on the next one everybody one two three four five six seven eight nine nine to go Timmy Stop Timmy eight to go Here we go There's Tate Biggsby two at one at ninety nine Tyree Wilson, Cedric Tillman, DJ Chirk, Purple Ice, Josh Dobbs to two twenty five Silver, Bobby O'Karaquay, Orange to two forty nine George Kittle, KJ Henry and Stetson Bennett Really Josh Dobbs the story of the season Yeah for a couple of weeks there he was Silver, Emmanuel Forbes, Purple Ice to two twenty five Jalen Waddle for the Dolphins Jalen Hyatt and manual Wilson That's Dawson Knox to sixty Nice one there for the Bills, Zach Evans and Charlie Jones Jordan Love, Blue Ice, Trayvon Williams to ninety nine Three Stevenson, Isaiah Foskey Flacco has assumed the rule true. I guess that's true Silver out at one ninety a St. Brown, Dwayne Bow to ninety nine. That's a throwback That's on that one there, Blue Ice, Sensational Signatures Silver, Chigaquanqua, Blue Ice, Kenny Pickett to ninety nine J. Kainer, Jameer Gibbs, Rookie There's CJ Stroud for his Matic and DJ Turner to one seventy five Nice one there, congrats on that on the Hyper. Derek Hall and Juju Brence Purple, Dawson Johnson, nice one there to one twenty five Congrats on that Rams, Josh Downs and Michael Wilson Silver, Fireworks, Derek Henry, Hyper, Hayden Nurse to one seventy five Michael Meyer and DJ Turner Emergent is Amon Ross St. Brown Kenny McIntosh, Silver Rookie Otto is going to be going to the Seahawks, congrats on that Seattle Kenny Nice one there, Kenny McIntosh, Parrish Johnson and Tradeshawker Victor with the Cowboys in nineteen, thank you buddy Vincent with a spot in Flawless Collegia as well That is going to be one, two, three, four, five, six, seven ago in the next one Alvin, who did you take? I don't think I saw uh I didn't get to thank you for your order Alvin took the Titans. Thank you Alvin. Appreciate you brother Um, all right, let me do this real quick. I forgot to tag this off 18 There's Micah Parsons Legerius Snead to seventy five on the green scope and Zay Flowers That is a Travis E.T.N. Jr. Purple is Emmett Smith to one twenty five, nice one there Cowboys, Nemoze, Zach Harrison and Cam Smith That's Drew Ledsoe, nice one there, 149 for the Patriots DTR and Cedric Tillman Silver Jordan Love and Purple AJ Dillon Nice one there to 125 Devon Achan and Marvion Overshown Silver is Jake Ferguson and Jonathan Allen to 175, you're not wrong on that Travis True Will McDonald and Luke Musgrave Flacco's your feel-good story, Watson's your oh boy Nice, how about a color blast price y'all? Congrats on that Panthers. Let's go man. Here we go. That's what we were waiting for Something like that.  Take that all day color blast number four In the entire set Very nice What's wrong with that at all? Get that right into a mag Kyle Duggar to 199, Abba down Kanda and Lucas Van Ness CJ Straub, Prison Break That's an auto of JSN. That's a good box man. Jackson Smith and Jigba Rookie Auto Silver for the Seahawks Yeah, yeah, Diabi and Elijah Dawson I'm a nice Bryce young today. That'll be honest with you Yeah, I agree. Bryce Young is a total by low right now. Total by low Mark Rizmatic piece orange debo to 249 for the Niners, Klajia Kansy and Chase Brown Honestly, yeah Because especially going into the next season with the new head coach and Hopefully they figure it out So, Erwin Johnson. True. So, 99 is Logan Wilson Blue Ice, Kendra Miller and Sam LaPorta Silver Devontae Smith all-purpose Blue Wave is Luke Soonbaker 2199, Tate Banks and Dante Dion Blakes Silver Portals, Jamar Chase Jake Hayner Orange to 249 for the Saints JSN and Tank Bigby Tank Bigby Not till tonight BF. We'll be doing them on the main channel after group breaks tonight with Forest Silver, Deontae Johnson. That is an auto of Michael Wilson Going to the Cardinals. Nice one there. Congrats, Arizona Devon Witherspoon and Anton Harrison and Kid Reporter. Yeah, absolutely BF. You got it buddy You got it Seven to go everybody on the next one Broncos Raiders Patriots Giants Jets Bucks Commander So nothing outside the Raiders and really nothing very very expensive, which is kind of nice On the next break Silver, Tyjay Spears-Rookie Purple is Dallas Goddard to 125 for the Eagles Tully Tui Palottu, Jonathan Mingo Algeria Sneed, Silver Chris Rodriguez Jr to 99 is For the Commanders Bryce Young and Jaden Reed Prismatic Aaron Rodgers to 149 is Jalen Thompson Nice one there Kenny Maddox and Josh and Felix on Blique Luzon Silver Bijan Rookie Zane Jones to 175 Nice one there for the Jags, Christian Gonzalez and Zach Shardnack Hopefully he can be back healthy next year Gonzalez No Zay Yeah, true Silver James Winston Purple Ice Sam Hall to 225 Yeah, it's a little bit echoey today Timmy Rishi Rice and Dalton Kincaid Silver Equinamia St. Brown That is a one or seven of ten Brian Breezy Gold Auto Wow Nice one there Saints, congrats New Orleans That's dope dude That is dope On the end, Barry in on that All right, so now we'll get that into a MagSaints A play just fine So we'll Zay Flowers and Devontia Silver Lockdown as Jalen Phillips Absolutely some big man love He's like the highest ranked recruit that came out of I think he lived in South Carolina He's like the highest ranked South Carolina recruit of all time Wow 225 back to Yari Morban Overshown and Will Mcdonald That sounds about right for South Carolina Because you don't hear a lot of names coming out of South Carolina Yeah Yeah Purple Power Devontia Adams to 49 for the Raiders Ivan Pace and Goose Vaughn Travis Etn, Jr. to 49 Nice one there for the Jags Orange Byron Young to 249 Grats on that Raiders Luke Musgrave And Yaya Diyali Silver Emergent Monroe St. Brown That is Vinny Testiverty To 49 on the Purple Power Auto Nice one there for the Jets That's pretty cool Vinny too Yeah, it's right for the time being That's going to be the situation I apologize Jalen Carter and Shawn Clifford See if that makes any of the difference Thank you Mr. Anthony Picking up the Chiefs in 21 Appreciate you buddy Again, five, seven to go in the next one Five to go, seven to go Come on, number Of some sort Yeah, no People have made us aware which is good Marvin Jones, Jr. to 75 On the Green Scope For the Lions Peter Skoranski And Whitton Johnson Yup, still seven to go Seven to go Still seven to go, everybody Still seven to go on the next one And that'll be coming out of a fresh case as well So fresh New ice is Derek Forrest, Jr. to 99 For the Commanders Elijah Dawson and Tay Banks as well Looks like a thing about Yeah, right, exactly It's to Damion Clowney You'd be like the best one So a lot of the guys either went to South Carolina or Clemson That's where Breezy went Yeah, no problem, man You got it It's an awesome one, man Brian Breezy Very nice See the first round here too That's a nice one, man It's my first Gold Auto I pulled this year Actually, I think at least Gold Rookie Auto Like true Gold Rookie Auto For sure, it's the first one For me JSN175 on the Hyper Nice one, Seattle For work Charlie Jones And Jay Caner T.J. Watts Pipe And At Christian Kirk Two 225 per voice That's Chase Brown and Kendra Miller I appreciate that Appreciate that, Sammy Thank you, buddy Thank you Appreciate that a lot, man Purple Ice is James Conner 225 for the Cardinals Jameer Gibbs And Derek Hall Sam got fans Sam's got fans, Zach True Silver is Harrison Smith Orange to 249 Zach Charbonnet For the Seahawks Sam LaPorta And Devon Williams Silver Tyler Boyd Green Scope Mazzie Smith The 75 Nice one there for the Cowboys Anton Harrison And Bijan Rookie Bijan Bijan Orange, Brandon Eyup 249 JuJu Brence And Paris Johnson Jr Jamar Chase Got James Cook Second year for the Bills Silverado Man loves it That's true Man does love the Ravens True That's got Travis on board Right there Easy That's all you gotta say for Travis Travis is in Justin Herbert for his Matic Is Green Scope Darren Waller To 75 Nice one there Thank you T. Chen with the Falcons in 20 Victor M with a couple of Prism Random Spots Appreciate you as well Miles Murphy and Erica Gray Silver Lockdown T.J. Watt Patrick Peterson to 99 Jalen Hyatt and Cedric Tillman Silver's a Flowers Nice one there Congrats on that 299 is David Montgomery Blue Ice for the Lions Basin, Stetson, Bennett That's Gold RPA Come on Gold RPA There we go Big name Come on baby Come on For a one time Silver Chris Olave It is Michael Wilson Not bad 10 of 10 Gold RPA for the Cardinals Hell yeah dude Yeah at all I am in on that I love the RPAs in this When you get a really nice one They look clean man The one of ones look super clean The patches that are in some of the The lower numbered ones are awesome as well So congrats on that There you go Arizona One on the Gold RPA Very nice Very nice Tariq Stevenson And Isaiah Fossum Silver Emergent Desmond Ryder Purple John L. Wade 125 Nice one there Manuel Wilson And Zach Evans Get 7 to go on the next one Everybody 7 to go Nice Thank you Jesus man Man That dust That prism dust Brutal Silver ETN Orange Ron Dale Moore to 249 Manual Forbes And Pukinakua Rookie Silver Rookie Is Nolan Smith Blue Wave Tyree Kill to 199 Eric Gray And K.J. Henry Virgin Tony Pahler Navy Camo's Garrett Wilson 225 And congrats on Jets That's pretty sweet 8 to 25 Tyler Scott And Brian Brees Justin Jefferson Throwback Silver Josh Reynolds Orange to 249 Stetson Bennett And Sariq Stevenson Silver is Andy Dalton Does he really never? Wow K.J. Henry Going to the commander Silver Rookie Auto Congrats on that Nice one there Commanders Henden Hooker And Joy Porter Jr That's kind of surprising That was never a first team all pro Who wanted all those years then Yeah Actually Kelly Jim It must have been Jim Kelly No K. von Zippen Van Jefferson 299 For the Falcons On the Blue Ice Bass And Jack Campbell Bass Marino Probably as well Earlier Silver is Bouda Baker That is John Randall To 125 Evan Hall And Clayton Tunes George Kato Red Wave Eric Gray Rookie For the Giants To 149 John New Benton And Josh Downs Silver Prison Break Jameer Gibbs DK to 175 There's Aiden O'Connell And Darnell Washington Silver Ipe Is Justin Herbert Nice one there for the Charmers Nice Aiden O'Connell There we go Silver Rookie Auto There you go Raiders Congrats on that Very nice Taking Aiden O'Connell all day First O'Connell of the day as well Michael Wilson And Michael Meyer Is that a sign? Every single break Is it going to have an Aiden O'Connell now? Cool Let's go That'd be sweet Prisonatic Fields Blue Wave Is Kendra Miller To 199 Tank Dell Rookie And Chris Rodriguez Jr That's Karim Huntz To 199 Nice one there, Browns DJ Zerner And Will Anderson Very nice Will not be a terrible sign at all now We're down to five to go in the next one, everybody Thanks Thank whoever took spots real quick Barton with the Giants in 19 and 20 Thank you, buddy And Richard with the Patriots So thank both of you Appreciate that Thank you guys Broncos, Raiders, Jets, Bucks, Commanders Five to go The next half case of Prism Five to go We've hit some pretty massive cards today already too It's been a good day of breaks Solid all around Very solid all around Kind of all over the place too Yeah What teams are hitting What teams are hitting what It's not consistently the same team No, right, exactly It's switching up each time Man, look, Panthers and Saints And Raiders and Cardinals They're calling this one One of the brand Not till tonight Not till tonight, Morales They'll go at Jamar Jates Orange, Tyler, Algiers Two Two, 49, Cajun, Muti and Marvin Menz If you go here to the break schedule I'll drop you a link to it really quick You can see what time They're expected to go Just scroll down And it'll automatically adjust to your time zone If you're not in the Eastern time zone too Which is very nice Silver of Gino Smith Purple Power, Sam Laporta There we go To 49 Lot of Laporta coming out today Let's go, man There you go Detroit Take that all day Very nice Charmene and Rishi Rice Rookie Mag number five on this half case Again This case has produced 10 mags And overall Which is kind of insane To think, yeah Silver box, Yari For the Packers That is going to be an Orange Keanu Benton To 249 Cincade and Ivan Pace Purple to 125 Justin Fields Hello Saints What's going on, buddy? Saints Jalen Carter and Jules Vaughn What's up, brother? How we doing? How we doing? Good to see you as always Silver here, another Navy Cambo coming up here It's going to be Jason Kelsey That's cool, man It's 25 Congrats on that Eagles Take that all day There is Davis And Dorian Williams Purple, Drew Tranquil To, uh, one 25? Jared Holland Schoolmaker I mean, Prism has been pretty solid Overall, I would say, Saints There's a couple of decent teams still left as well That's all we got this morning Yeah And then tonight there's Bowman There's more Prism There is What else have we got tonight? Bowman, Prism I think Definitive tonight Upper Deck Goodwin Champions Flawless Collegiate Football A little bit of everything tonight, too Nice little smorgasbord Oh, yeah Thank you, Robert Picking up the Jets and Commanders Down to three you go in the next one now We are down Forest, Junior Javon Curse to 175 Down to three CJ Stroud Three left in the next one, everybody That's it Three to go Drop you a link to that real quick as well Broncos Raiders Bucks That's it Broncos Raiders and Bucks Three to go on the next break Again, that'll come out of a fresh case That'll come out of a fresh case of Prism Silver as Andy Dalton Andre Reed to 149 Nice one there for the Bills Congrats on that Buffalo Sean Clifford and Peter Skoronski Josh Jacobs Keon White to 199 Is Blue Wave for the Patriots Taj J. Spears and Tully Tuiikolotu That is a Blue Wave of Tyron Matthew Quinn Johnson and Bryce Youngbrook Silver, Prism Break, Jamiro Gibbs That is a Goose Vaughn to 25 On the Navy Camo Auto Nice one there, Dallas That's awesome, dude Doose Doose Take that all day All day on Navy Camo Auto Never a bad thing at all John Domingo And Christian Gonzalez And last pack of the break Good luck here, everybody Do a quick recap as well We'll be on the next one Blue Ice is Josh Allen to 99 Orange to 249 Sirik Wollin Congrats on that Jaden Reed-Rookie And Kenny Mackinsosh All right, quick recap here, everybody To 99 we've got Barry the Fair Josh Allen Ben Jefferson Patrick Peterson David Montgomery Derek Forrest, Jr Chris Rodriguez Logan Wilson Kenny Pickett Trayvon Williams To 75, Darren Waller Mazzie Smith Marvin Jones Legerius Snead To 60, Dawson Knox To 49, Devonte Adams Travis Etienne To 25, Kelsey Garrett Wilson We've got autos KJ Henry James Cook Michael Wilson JSN Kenny Mackinsosh Andre Reed Dwayne Bow Vinny Testa Verdi Duce Vaughn Magtars, we got a lot of them actually Sam Laporta to 49 On the Purple Power True Rookie Silver Aiden O'Connell Rookie Auto Gold RPA Of Michael Wilson For the Cardinals And a Gold Rookie Auto Brian Breezy For the Saints First Rounder And of course the Colorblast Of Bryce Young Going to Panthers Yeah, it really was Pancakes That'll do it for the break, everybody Thanks again for the fill Three to go on number nine


What's up everybody Jason here from jazbyskatesbreak.com this last little pack filler fills the break This is for giving away spots here in the 15 team random number block For opulence pick a team number two, and we're giving away four spots in there So again a way this works guys 30 spots everybody gets a random team High risk high reward we're gonna first randomize because we're naming the teams the trip of the hits out of the cello Or sorry not the cello the Chronicles fat pack. This was Chronicles fat pack NBA Round to number 185 then after that will randomize customer names again and the top four out of the 30 win a spot in the 15 team Pick a team number two opulence random number block So good luck guys. Let's do the break first. Let's roll it two and a five seven times One two three four five six seven Robert down to Robert seven times here one two three four five six seven The Cavaliers down to the Sacramento Kings All right, so there you go Stick with you guys just a quick glance We got the Lakers also the Grizzlies and Richard at the Pelicans Bible so cool LeBron James Steffan Curry Kobe whites Jackson Hayes James Harden Tyler he wrote who stayed roaming the line for RJ Barrett and PJ Washington Recon brah. So there you go Now top four get in let's roll it six and a two for eight times one two three four five six seven and eight times top four get in Robert you are in Michael Hansen Roberts and Richard Congratulations, these are $300 spots were given away guys So six and a two for eight times top four get in now in a separate video guys I'm gonna run the randomizer for the 15 team round number block and then opulence pick your team number two. Appreciate you guys


Hello, this is Christian. Welcome to Angular. In this video, let's do the put or update of the credit operation using this HTTP client RSJX library in Angular. So this is a scenario here. We're going to send a, we're going to fetch, well, first we actually fetch the data from the remote server first. And we display the data to a form page. We click edit. And then we're going to edit that information here. We send that off to the subscription and then the Angular service will be sending that put request to the server and update that data. So let's go and see how this is done. Okay, so here's our app again. Last time we created the display and the add. We're able to add a one extra flight down here. And so this time we're going to go and say, you know, click on this. And then we're going to edit that information here. And in the form again, we're not validating at all, we just make sure everything, or I sort of think it's going to be correct. And so let's go and see how this is done. And this is the service. So we're going to invoke this function down here. Much if we don't have one year, we're going to create one now here. And so when we update, we actually need the ID number, right? So kind of similar to the get or delete here. So I'm going to put right here, copy this and duplicate that right down here. And this would be for update, just update one. And so it would say update flight. And it takes the ID and also the payload. Okay, so two things. So this would be the flight of type flight. And then we're going to send in the URL with no ID. Actually, it does right now with ID, this ID matches the ID. And then the second parameter is the payload. In this case, it's the flight information. Okay, so let's see. Let's see here, what's going on overload matches this. Oh, yeah, this is going to be a not gap. It's going to be a put that's why. All right, so here we go, we got that function all set up. And we're good here, you can close this now. And let's load our edit. This is the one here. This is the source and this is HTML. Okay, so we have things all set up here. When we submit this form, going to send in this f object that ng form to the submit function is going to get all the data. Now we need to bind to a data. Okay, so as you can see, nothing's binding here yet. So we need to fill that in. And then the red bottom here and see when we submit the submit type. Yeah, so we just need to bind this data here. So first, let's do it and fetch our service. And I'm just going to put it here so it doesn't air out, but we're going to change this. So we need to get the ID number. That's one thing. And this time, because we're fetching data remotely from a different server, we cannot use this use the snapshot. Okay, you want to use the asynchronous call, which means going to get it from using a different method here. Very, very identical to the snapshot, but we're not going to use that one. And also we're going to inject the services in here as well. So let's do that injection first. First, I'm going to inject the flight service. There you go, we got that. And then to get the parameter on the URL and the ID, we need to also inject another one called the route activator router, activator router. Okay, so this one here. This token allows us to fetch any parameter or all the parameters in the URL. And one of those parameters that we want is the ID. And that is what we set inside our router, right, if you. So here's the route when we pass to the edit, and it fetch an ID. So this is the field that we want to grab. Whatever you call it, this is one of them if you can have a lot of IDs or a lot of fields, you can fetch those as well. And and use that. So now, and that's what this ID is for. Okay, it's the actual number of this route. Okay, so in the ng in it here, what I'm going to do is I'm going to get this route ID first. So I will say this dot route dot param app, okay, we're going to call the param app here. And this param app, we have to subscribe so you can see subscribe again. And we subscribe, you can see that the observer is, you know, send back some data. Okay, so, so here we have really a parameters object, usually have a lot of them, we're going to pass that to the function, and then I'm using the error function here. And all I'm doing just one data. So it's not a big deal you could have, you can you have a single line output here, separate line away. So I'm now this parameter here has access to the parameter I mean, in the URL, I'm going to sign this ID from this parameter group. So this ID is equal to the programs that get and the get function here, you can see the string of the field or properties, or token, right, URL token. And that's what we're going to get. And there's an error here is what it says. ID number, and we got a string. Yep, so we say it's a number, but we're getting a string. So it's a conflict here, right, so either you can turn this off to say any. But we don't want that because the actual ID and the database is a number. So you want to basically just cast this to it. Okay, you wrap the whole thing, and convert that to integer, and they'll be assigned to enter, and we're going to go. And actually, this is not, this is the function, and then I need to close it with the curly, right there. I have too many curlers and that one for this one here. That's for that. And I need one more for that. Yeah, it's a lot of them. And then that's the subscription, we're going to close that and this is extra one. Yeah, that's why it's easier to put in the separate line like this. Okay. So now we are done with that one. That's all I'm doing. I got the ID already. And then once you get that, then you can call a function maybe like to load the data. So I guess I just call it load function here load data. We'll get this data from the service. Okay, I'll create it right here. Load data. And this function is going to call this service and then pass the data of the ID to it to fetch the data back. We assign that data to this flight data here. So let's say this dot flight service dot get we need to get first get a single flight information. Okay, and then the ID is this ID that we just we see from the URL. Again, you have to subscribe to okay, if you don't subscribe, you're not going to get any data back. So it won't work. That means I have to go here and put here the dot subscribe you put in separate lines easier to see that way. And then the data coming back in the observer is going to be the data, the payload. And then we can set this flight equal to this data that came back. Okay, so this data here is the one that is sent back from the server based on the ID we sent to it. Okay, so now then this will be populated and so instead of just the empty object here, I'm going to assign this to as a class. And so I don't want to say this either if I just do this, I might get an error. This is the flight class for imported. This is the class that we have. And that's this one here, right?  And it's going to be displayed on the browser already. At that time, all these that you ID and so we're not not there yet. So you might have an error. And so now we got that done. And then so, so here I need to say, instead of assignment, I mean, type to say a new flight. It's object. Okay, we'll test the other one if, if it works, but usually this is what we may do. Okay, for edit, you have to pre-populate this with data first, and then this comes later. So now, in our form, we need to bind this data now. Let me close this over here. So the flight ID needs to bind to, so I do the two-way data binding. Okay. So ng model is combined to the flight.id. That's the one. And I'll just copy this, put down here for the, this is the flight number. So flight number. Oops, flight flight number. And then this one here is the airline. And it's really hard to see. Let's do this. Okay. This one here will be the trip type. And this one here is departure airport, arrival airport, departure date, and then arrival date, return date, I'm saying return date. Okay. So I think that's it for this one. Let's see if it loads. Let's go check it out. Browser. It did already. It was great, right? So again, if you refresh it, go back to the flights, go to show flights, and let's say I want to edit this one here. So there you go. It grabs that information here. I go back and do number four and so on. So it loads very beautifully. Now I mentioned earlier that if you don't subscribe, it's not going to work. So for example, if you go back, and if I don't subscribe to this function, if I just say, you know, I terminated that here. Okay. And if I leave that out like that, and if you do something like this, that flight equals that, right, it may not work because I need to subscribe to that. So type of any and have a conflict because it's a different type. So I have to maybe ask a flight. That's observable. Yeah, it's a different type. So if you don't invoke it, it's not going to work. Let's see here. Okay, I'm going to force it to type any. And so if I save this now and go back again, let's see if it lets me. Okay, so you can see that no data comes through because we didn't really invoke it to make it happen. So that's why it's important to make sure that you subscribe to that in order for it to work. Okay, so I'm going to just undo this. So we subscribe to that and then we're good here. And so now when we edit, we click the submit button, we're going to do the edit here. And then we have to also submit to be true once we're done. So again, when you submit the changes, you have to subscribe. So flight service, we're going to do a update and update takes two parameters. The ID, so with this ID and the payload will be just the f dot value. Okay, all the values coming from the form. And again, subscribe. So the data is the one that's coming back, right? This is a function, but we need that parameter. And then I do two things. One is I'm going to say this stuff submitted is now true. And that's it really. But we also can console log the data, the original data. So form the f dot value and then also log the data coming back, which is in the case of data. I think maybe just the same data coming back. So let's see what happens. All right, so let's go into the site and refresh our page. And I'm going to edit the first one. Just change that to one, two, three, four, five, six, seven, eight. Pretty long one and submit. It says submit already. Let's go check it out. And there you go. We change that to that field. So it works. And I can change it back again to just one, two, three, four. Actually, before I change it though, I want to show in the database to make sure it really does work. So we change that to one, two, four, five, six, seven, eight. I load that and you can see that the field here has been changed because the new update. So now let's go back and change it to one, two, three, four again, submit, and then it's back again. So last thing is again, just make sure you subscribe. If you don't subscribe, you just leave it like this like that. It's not going to work. Okay. If you just do like that, let me turn this off. And so if I save this, even though I don't put the true thing here, well, let's say this that submitted is true. The fourth set to be true as if it's been submitted. And now let's go back and edit the first field. I'll put here, you know, five, five, five, five, click submit. It says successfully added. It says submit it, edit it, but you can show that it didn't change, right? It didn't change the data. We can also show the database, refresh it. You see that it did not reflect that here at all. Okay. So make sure you really invoke that function at the service using the subscription or it won't work. Okay. That's really important here. So that is the put operation or edit. And if you have any questions, just let me know and I'd be more than happy to answer your questions.


This episode is brought to you by Gamedeus, the god of artistic motion gaming. Hi everyone, today we're going to be talking about the forest. If you like the survival aspect of Minecraft, but you're looking for something a little more...grown up, then you might enjoy playing the forest. The forest is a survival horror game that takes place in the woods after a playing crash. If you play the game solo, then you're just one man trying to survive the game alone. If you co-op, you're all the same man trying to survive together. But you're all the same man, so are you really alone? I'm confused. Hopefully in an upcoming patch they'll introduce new skins for co-op players. It's a little weird looking and talking to myself the whole game. Chop, chop, chop. But I gotta say, I do look fly and camo. Anyway, back to the survival part. Little do you know, but you should probably expect, you're not alone in the woods. There's creepy cannibals out to find you and eat you one bite at a time. And if you don't make weapons or traps to keep them away, they'll getcha. There's an entire survival book that helps guide you through the days and the nights. You can build shelters, traps, gardens and weapons. Weapons can be upgraded in multiple different ways. For instance, you can use the teeth of your enemies to upgrade your attack. Yeah, I said teeth. And that's actually not the grossest part. I feel like this game was pretty easy to pick up thanks to my expertise in Minecraft. I already knew to start collecting things during the day so I could build up my fortress at night. Cannibals aren't as scary as creepers, but they're pretty darn close. Building shelters and stuff is actually pretty easy. You just open your book, click what you want, place it down and then put resources in it as you gather them. Weapon crafting is a little bit tougher as you have to either look up the recipes or get lucky guessing. And although hunting for animals is rather humorous, it's a little bit hard if you don't have a bow. You have to swing your weapon in the right direction to kill the animal and most of the time you miss. So I normally just result in eating berries. I had a ton of fun playing with Mike and Favio. But with the three of us, we did feel rather accomplished pretty quickly. And we hit a point of, well, what do we do now? Obviously we didn't accomplish half of what there is actually to do. But once you build a house and take out an entire mutant village, you're feeling pretty good about yourself. This game is constantly updating and there's still actually an alpha, so I'm sure there's a lot of really great things still to come. Overall, I rate this game 16 severed cannibal heads. Thank you guys so much for watching. As always, I hope that you did enjoy this. And if you would like to see the full gameplay, do go check it out on my channel, Brits Games. The link is down in the description box below. I will see you next week. Thanks for watching. Bye. Hello, and let's do roll call. Let's make sure everyone's here. Okay, we have Favio. All right. Take a Camo Wonder and then the Burtney in there and we are home. Camo Wonder. Yeah, we're all practically the same person currently. There's creepy cannibals. Impulse is produced by the Freedom Network. Ever wanted to earn revenue from your videos? Freedom offers a great partnership program which includes access to hundreds of thousands of audio tracks, sponsorships with great partners, and most importantly, a no lock-in contract. You can leave at any time for any reason. We accept everyone, both big and small. For more information, click here or visit the link in the video description.


It's good to be able to see you this morning and to worship the Lord with you all So my name is Mark Mudge and I am a missionary in Guatemala City and have the opportunity to be able to give a missions report to you all this morning and so what I'd like to be able to do in this morning is to to be able to speak about the spiritual war and Ephesians 6 for a few minutes and Then to be able to give you a report about how things have gone in the past Four months or so since the last time I was here. I was actually here not that long ago, so Please be patient with me. I've got a mix of Spanglish going on in my mind and so sometimes it's hard for me to communicate in a clear normal way so Please be patient with me this morning and the sermon and in the Sunday school and I'll try and speak in a clear way for you Let's go ahead and open with prayer and then we'll begin with the update. Okay. Let's pray Lord God, we want to thank you for the opportunity to be able to be here in your day What a blessing it is we want to thank you that We're able to worship you in person and we thank you for this grace We remember this is your day that this is a time set aside To rest one day out of seven to worship you to focus on what you desire to hear your word to Grow in your likeness Lord God, we pray that you would help us to grow in our understanding of the gospel and What it means to obey you to live for you? Please help us to exhort one another as we see the day coming Lord, we pray that you would help us to be able to encourage one another to love and good works in this day please help us with our conversations to think about your word and Please help us to love you and your people today We pray for this update that you please would help me to be able to glorify you for the great things you have done Lord, we pray that you would help us to grow in our service of you So Lord, please bless this time So that we would be led to worship you. Thank you. Amen so once more I'm Mark Mudge and I used to be a member here with my wife Ashley for about 10 11 years and We are now missionaries in Guatemala city Guatemala and we have About or we've been there for about five years now four to five years and so What we have is I'm gonna try and work through a slide show in order to So we go with the next slide brother We Have been in in Guatemala city for about four to five years now and We're this is a picture of our small church in Guatemala city from this this past year And so if next slide, please We're in Guatemala, which is just below Mexico and I'm showing you this map not because most of you guys know where Guatemala is but I'm showing you this map because it becomes more helpful later on with some of the report the Guatemala is a country about the size of Tennessee just below Mexico and It has a population of about 16 million people Maybe about four million in the capital So it's about the size of a Philadelphia in the size of how many people are there in the center it's kind of hard to see south center there is the capital in a mountain range and There's some at the country is made up of departments and then which works out kind of be like counties About the size of counties here and so there's some It's kind of hard to see but a Orange-ish reddish want to then you see up to the right near the border of Honduras named secapa is There's a department which one of the brothers or there's new members from the church from there So maybe I'll cut I thought I was gonna have a clicker. They'll be able to move back and forth But I'll try and remember this map and it'll become more applicable later on when we talk about members Okay, if you go to the next slide blues So we've been there now since we moved in 2016 September. This is a picture from back then our very first Sunday Benjoo and I looked younger back then and So we're we're very thankful to be able to Have had the grace to be able to be there these four to five years now so let's begin to Open up the scriptures into Ephesians 6 Ephesians 6 We're gonna read Ephesians 6 verses 10 to 20 And so when we consider that we've been there four to five years now One of the things that's a very important is perseverance in the Christian life Perseverance in the ministry and so the Lord Jesus helps us Guides us on how to persevere in the Christian walk In Ephesians 6 verses 10 to 20 So I want to be able to begin this update with Looking at this text and remembering some basics about it. Let's go ahead and read chapter 6 verses 10 to 20 We'll begin it will briefly cover this text and then we'll get into more detail of report About what's happened the past four months and then questions God willing So Ephesians chapter 6 verses 10 to 20 the word God says finally my brother and be strong in the Lord in the power of his might Put on the whole armor of God that you may be able to stand against the wilds of the devil For we do not wrestle against flesh and blood but against principalities against powers against the rulers of the darkness of this age Against spiritual hosts of wickedness in the heavenly places Therefore take up the whole armor of God that you may be able to withstand in the evil day and having done all to stand Stand therefore Having girded your waist with truth having put on the breastplate of righteousness Having shod your feet with the preparation of the gospel of peace above all taking the shield of faith With which you will be able to quench all the fiery darts of the wicked one and take the helmet of salvation The sword and the sword of the spirit, which is the word of God Praying always with all prayer and supplication in the spirit being watchful to this end with all perseverance and supplication for all the saints for me the utterance may be given to me that I may Open my mouth boldly to make known the mystery of the gospel for which I'm ambassador in chains That I may speak boldly as I ought to speak In this text we can kind of see three clear divisions in verses 10 to 13. We have an introduction to the spiritual war in Verses 14 to 17 we have a practical explanation of how to put on the armor of God and Then in verses 18 to 20 we conclude with the spiritual war with the importance of prayer and the preaching of the gospel and So Paul begins this section with finally my brother and He's beginning to bring the the epistle to a close He's explained three chapters focused in on the doctrine of salvation and union with Christ the doctrines of the grace of God revealed in the election of the saints and his prayers for us to know Christ and Him giving us new life in Christ How the church is reconciled with Christ and with one another He's explained about the wonderful mystery of being able of preaching the gospel to all the nations and How the gospel and union with Christ is evidence by a clear and distinct sanctification union in the body of Christ Serving one another in the local church and a definitive growth That's seen in the family seen at work seen in marriage seen in raising children and so then we get this last part and defeat in the book of Ephesians and In verses 10 to 13 we have an introduction into the spiritual war Introduction to the spiritual war so spiritual war when we say we use it war. It's a conflict There's a great conflict and there's a great goal. There's a great enemy when we have a conflict it means that We have a conflict against Satan and a spiritual forces there at work and We have but we have a great goal War always has a good goal is to have a good goal. It's the a just war and So the goal in this war is the glory of Jesus Christ the glory of Jesus Christ Through the preaching of the gospel the salvation of souls and the perseverance of the saints So this is a very clear and distinct goals that we want to glorify Christ and enjoy him forever But we have great opposition So we must be very clear that our goal is to preach the gospel to the lost and to Preach the word of God to the saints so that we would persevere in the faith And so then we have an instruction here and how to do that in verses 10 to 13 an introduction to that so he begins this last theme in verse 10 finally my brother and be strong in the Lord and And in the the power of his might so he focuses on us being strong our responsibility and Yet we're strong by dependence on the Lord And so we see that when we're weak then we're strong When we're emitting our need for the Lord and His power and his the work to be done by his Strength by his grace. That's when we're actually strong. And so then we have a practical Exertation verse 11 put on the whole armor of God That's how we're gonna be able to be strong and then we have the purpose and In verse 11 that you may be able to stand against the wiles of the devil the devil wants to work with all kinds of lies lies in the world lies in systems of religion lies in philosophies of thought Ways that are common to can be Some common ways to communicate that you see in the TV and social media That you hear at work you're here in school That's evident in verse 12 that we don't wrestle against flesh and blood But against Principalities powers against the rulers of the darkness of this age against the spiritual hosts of wickedness the heavenly places We have four terms describing demonic powers here Not in such detail that we can organize and have a clear structure But in a general way to know that they're organized And they're prepared in the spiritual war In order to pump out their lies and the world is gonna drink in all the lies these demonic lies and this is really what's behind Philosophies that are common in our country and in churches that are false churches sadly And so we see we this is how we won't how we wrestle. It's a spiritual warfare. It's a truth war And so in verse 13 we have the the call again to take up the whole armor of God That you may be able to withstand in the evil day and having done all to stand So here we see that focus at once again on with standing standing firm You get the image of someone on the the wall of a castle Having to defend against the the hordes that are attacking and trying to overcome the castle And so how do we do that then? If we have this introduction in verses 10 to 13 the big picture the big view Then we have a verses 14 to 17 to describe how to do that How do we continue to war in the spiritual war? How do we battle? We'll stand there for in verse 14 Having girded your ways with truth and so that we be going to go through the particulars of the armor of God so when we consider the armor of God There is a cultural background, but there's also an Old Testament background There's a cultural background, but there's also Old Testament background and you got to understand both a lot of preachers in this text we'll focus on the cultural background and How a Roman soldier was dressed and have it maybe a picture of a Roman soldier But it's important to remember that there's an Old Testament background to this then the book of Isaiah It describes a Messiah as being having these same pieces of armor and That it's really his armor That when we look at it and we look on the inside of the shield It's got Jesus Christ's name on it and that that helps us to understand to be able how to apply these things That the armor of God is not simply meditating on the gospel and it's not simply Living practical obedience in a practical steps. It's actually both It's actually meditating on the truths of the gospel and Applying those truths in your life And you remember how that's the way the New Testament communicates about how to grow in the Christian life Like in the book of Titus where it describes Repeats good works good works good works good works to the out the book of Titus, but it's all connected back to the gospel and Our union with Christ our dependence on him that we actually grow by understanding the gospel better and growing and Christ likeness and so we we see that those two those two things are not two different decisions, but really they're both applied Meditating on the truths of the gospel how Christ wore this armor in fulfillment with the prophecies of Isaiah and That it leads us to wear the armor it guide it teaches us that we need to wear Christ's armor and so as we meditate on the gospel and We grow in the understanding of how Christ everything he said was truth and He was a truth incarnate and as we meditate on that and his integrity and his truthfulness it leads us as Christians to Speak the truth and to have integrity To live in a way that's truthful and we have the belt of truth So if you want to learn more about that there's a little book by Brian Borgman and Robin Ventura called a spiritual warfare and It's an exposition of these these verses very clear very good explanation of The historical background, but also the Old Testament background to this text that helps us understand that it is The way to apply it is it's truly meditating on the gospel and applying it in a practical way both of those things and so we have this instruction of how to do that with all the different pieces of armor meditating on the righteousness of Christ and then living in a righteous way that is that it completely fits with that a True understanding of the righteousness of Christ imputed to us leads us to live righteously in verse 15 We remember how Christ Won our peace for us and How that leads us to have the gospel of peace ready on our lips in verse 16 Where we take the shield of faith and We're able to trust the Lord with all during all the lies of the evil one and verse 17 the helmet of salvation that Christ has won and And then that assures us and gives us an assurance of our salvation and we use the sword of the spirit and then lastly we see in the verses 18 to 20 the importance of prayer and Preaching the gospel in the spiritual war So why do we begin here? Well, it's good to begin with the scripture be focused on the Lord But it's also a key description of of how we're to persevere for how to persevere here in Orlando and how we want to persevere in Guatemala Continuing to grow in our understanding of the gospel and applying it and look at how loving our good shepherd is To be able to guide us on how to persevere not just to begin in the Christian life But to be able to persevere to the end in a very very clear practical way for a great goal to glorify Christ and enjoy him forever by preaching the gospel to the lost and Teaching the word of God for the perseverance of the saints So that's what we're trying to do in Guatemala. It's the same thing. And so let's Begin to close this part where we have a opening with the scripture and begin to get a report about the things that have happened the past four months So I'm going to explain it using some pictures some of what we've been teaching some ministry opportunities some of Testimonies of how the Lord has saved people and then we hope to end with some prayer requests and Some questions So now we'll some of the things that we're teaching we're going through we finished the book of Ephesians since last time I was here And took us about two years to go through the book of Ephesians and now we're beginning the book of Habakkuk We've gone about seven weeks into Habakkuk and We're gonna study Habakkuk today Overview I'm gonna try and preach seven sermons to you guys in one hour. We'll see how it works In the book of Ephesians it's been a great blessing to us to in our in Iglesia and torchant torchant to be able to study about how The gospel is key for our spiritual growth in understanding So we had a year of chapters one to three Studying the riches that we have in Christ and then we had a year studying chapters four to six on how to grow In obedience to Jesus Christ and glorifying him So we couldn't really see the centrality of Jesus Christ in the gospel In Habakkuk, it's the same. We're learning how to trust the Lord and how to have wrestle how to Have the struggle of faith how to wrestle with learning to trust God And have a respectful questioning of certain times in certain trials But not an accusing of God And how we need to be able to grow in the faith And so we've been studying those things Next slide, please Some ministry opportunities we've had We've had some opportunities to I've had an opportunity to be on the radio in Bolivia. That's on the on the right side That was definitely a different experience to be on the radio And but in that opportunity was opportunity to speak about missions and the goal of those times Was to be able to glorify Christ So I'll all begin to talk about missions, but I also want to be able to preach the gospel And a brief clear way, but then also be able to describe how is a what's a biblical way to think about missions particularly a great emphasis is focus on the local church And how missions should be focused in on the local church being missionary sent from local churches That great There's a great problem in many with many missionaries that they don't really understand what it means to be called to the ministry They a lot of people just think about Well, if I have the desire to be a missionary Then I should go and be a missionary and they don't think about being sent from local church And the blessing it is to be able to be affirmed In your calling By the means that God has given including the local church And so I had the opportunity to speak out missions And be able to make some of those emphasis In a biblical perspective Of what of how to do the work of the ministry and also be once you get there on the in the mission field Being focusing the work in on the local church many missionaries in latin america They they go and they move there and they have a sort of perichurch ministry That is not submitted to a local church. There's many missionaries. They don't even go to church And they're often in another country Maybe teaching the The true gospel, maybe they're having bible studies But it's very common. It's very common That they're not actually submitting to a local church in the country that they live So the goal was to glorify christ but preach the gospel But also talk about a biblical view of missions and that opportunity on the left side is a little flyer about a In a pastor's bible study from some pastors from honduras. So honduras is a neighboring country And I know a pastor there Uh, and some of the other pastors know Manuel Sharon So that was with a the church called estandarte De Verdan, which is banner of truth banner of truth reform Baptist church So we the pastor there has a a bible study with other pastors who are wanting to reform And learn about there tend to be pentecostals a group of pentecostal pastors who are wanting to Learn about biblical doctrine. So in that opportunity What we taught what I taught about was discipleship He asked the he asked me to be able to teach about that So a big problem with discipleship Is understanding what it means to be a disciple So I know that you guys are studying this once again in small group, right? What is a biblical disciple?  That's not that's not clear That's a great confusion about that like there is here In there's a lot of legalistic churches that have various levels to the christian life And so they think a lot a lot of pentecostal churches teach in latin america. They they teach about You reach another level Of when you get baptized or when you become more dedicated and they and some churches have a lot of levels. It gets complex. It's not simply carnal christians and dedicated christians. It's it's more like a A ladder system with some of these pentecostal churches So because the pastors are coming out of pentecostalism That was a big goal to make it clear that a christian is a disciple and the disciples are christian But then to also apply That biblical perspective of conversion to ministry in the church That that leads us to have a biblical understanding of what it means to disciple in the church And that we should be a church full of disciples who make disciples So that leads to a healthy philosophy of ministry as well Something that the pastors needed as well. So those were opportunities to be able to To teach next slide, please brother other opportunities. There's two brothers here One named denis and one named jair that i'm trying to disciple And so it's encouraging to have some godly brothers or zealous that want to work in the ministry They want to teach they want to preach they want to evangelize and serve the lord So two of those brothers are relatively new. They've both been in the church less than Than two years or two years or less So here's a what we're doing on wednesday mornings As we're going through the 1689 so One brother denis in the middle He was saved in canada And And grew in the faith in a church called grace life That has a pastor names james Coats james coats who was recently released from jail So it's a small world the church is not that big it's about the size of cornerstone Yeah, so he attended that church or was a member of that church for about four years three four years So he's has a good foundation of understanding of the bible conversion And jair is a good brother who's I've mentioned him before about a great encouragement He is to the church how lisa's he he helped change the culture of ontorcha in particularly giving us a great amount of Encouragement to love one another sacrifice evangelize And so they're both very zealous brothers And so we're saying the 1689 because the goal is to help give them a basic understanding of systematic theology through the 1689 So understanding doctrine in a systematic way So that's something that's very needed in latin america is a clear systematic theology next slide please brother so in this We're praying in the dark here, but Here's our weekly bible study. We don't really pray in the dark. That's a joke But what we're with a picture of is that we're studying the the book of revelation And we're we have a midweek service where we we pray and we're studying revelation verse by verse What what's been encouraging for the people is that they've mentioned how learning And studying verse by book in the book of revelation is it's more clear and more clear each week And that what they really see is that it is the revelation of jesus christ It is a book that really reveals christ not conceals christ and so truly understood that it really guides us In the spiritual war to see the lives of the devil And the spiritual truths that apply to the church So that's been a great blessing. We're right now in chapter seven So I will recommend pastor rick sermons. They preached a few years ago For you all to listen to to remember some of those things Can we go to the next slide please please brother This morning the brother that was in Jair who was on the far right of the three of the picture with the three of us He is teaching the sunday school in which is holiness Holiness by jc jc rile. We're going through that that book About a biblical view of sanctification So today he's teaching the lesson about lot About how how lot was a righteous man second peter says But he was not an example for us Sadly in his compromise and so there's a lot of clear instruction in that chapter in that book About how to make decisions in life Where you don't make them based on what's going to get you more money What's going to be better for the moment? And we don't want to be like lot And make decisions that are based on this life. We want to be pilgrims who are passing through So we learn about how to be holy so The brothers are very encouraged by this study on what is true holiness There's a lot of misunderstanding about holiness in latin america With all the legalism in pentecostal churches holiness is often thought of as a very outward thing How you dress how you talk what you do on sunday But not true biblical holiness That's evident in the heart and sanctification in the thought life So this study has been a blessing the people in the church have mentioned That it's been a blessing to help with their assurance of salvation They have a true biblical assurance. There's a chapter in that book on assurance I'm not teaching that class lee and the other brother jair are teaching that class Next slide please brother So this is actually an example of essentials class. I am teaching essentials class And what we have here is a couple Who is lives four hours north of the capital And they are participating in everything they can online Thursday night midweek and and sunday morning They are participating in the essentials class mostly by means of zoom But they have traveled to visit us and so They were living together for about seven years if I remember correctly And so through the essentials class They said that we've learned the true gospel and then we want to follow christ. We don't want to follow him in a Sort of a light Even gel cool or light gospel kind of way. So so here they're getting legally married Uh and it's part of their desire to follow the lord They've expressed the desire to try and attend as much as possible from four hours away So it's um, eric is the the the guy on the left and alejandra on the right And so I encourage them. Um, they both want said they want to follow the lord So I encourage them to follow the lord together and be be married And so that's our representative of the essentials class Next slide, please brother So here we have a picture of an evangelism group This was a trip to one of the counties or departments off to the northeast secapa There it's kind of like arizona It's very dry and hot But in the capital it's it's great weather Some of the best weather in the world Hawaii is the only place that I like the weather better than than guatemal city But in secapa, it's pretty hot and there's no ac because there's uh, very little ac So kassandra had a hard time there actually But uh, we went there To be able to have an evangelism time and that's where the brother who was saved in canada That's where him he's living with his wife and they travel every other sunday So it's about three hours away to church And so we had a church Uh trip to go out there and evangelize So we're continuing to preach in the open air We're continuing there's a little note on the left zone 15 And that's where the church is located. So we're continuing to evangelize around the church So we've had many opportunities to evangelism a couple stories the brother on the far right corner jair I mentioned him with the thumbs up He's preached the gospel to some people at work. And so he's invited a guy named lewis and wilfredo And so there are people who are in A sinful lifestyle of drugs and things like that. So we spent a night together preaching the gospel to them Trying to explain to them that That these their lifestyle shows that they're not christians And so one of the young guys his name wilfredo. He was convinced he was a christian because he Grew up in the church and his parents and his parents were pastors and then he became a youth pastor And then he left the church and lived in and been living in sin for the past six years And so he was just completely convinced that he was Had just lost his salvation He was still a kind of a christian If he died he'd knew he'd go to hell But he would still think he was a christian So it's part of the pentecostal teaching that is very common there about you can lose your salvation So because Most people are pentecostals or catholics Both of those groups teach you can lose your salvation So it's very rare to meet people who don't think that you can uh that salvation is secure in christ Or maybe i'll say that in a different way most people think you can lose your salvation So so that's an example of some current evangelism that's been going on next slide, please brother This is our new location. We're headed to God willing we're gonna move to a school Excuse me The week he get back I'm actually not there to help with the move. This is our last sunday today is our last sunday So I asked lee before we we We planned this trip. Is it okay if you do all the work for the move? He's a good he had a good attitude about it So the the picture on the left is the outside just through those double doors on the picture on the right And so where there's a we're going to be able to rent At with a 40 cut in Rental costs Yeah, so the lord has provided For us and that's big answer to prayer Also there there's also a balance between Finding a place. It's also relatively secure So you can get places that are Have a good price, but then it's in a rough area of town and so then people Are worried to think about their car being stolen while they're in church And then it gets to be a complicated thing So it's really nice to be able to find a place Where they can park their car within the property And not have to worry about it being stolen And And be able to worship the lord without thinking about those things And so this is actually a school that ashley's family Runs So we're thinking the look we're very thankful for the opportunity to move We've had many mini mini ministry opportunities Studying through the the books of aphesians abacus opportunities in radio To serve other pastors opportunities in discipleship teaching the book of revelation studying the The book of holiness by jc ryle. We've had many evangelism opportunities We're moving this next sunday god willing Next slide, please And so some challenges. I know recently I was thinking about the way I give updates here and that you know, I only talk about good things is one thing I noted and never talk about some of the difficult things So difficulties what's been going on difficulties? One is a difficulty here that you that many of you know and many of you've been loving that are that my father-in-law is very sick And so with liver disease and so I want to be I'm very thankful to you all for Going and preaching the gospel To my father-in-law and so purpose of this trip why we're here just after form visiting you all four months ago Is really to spend time with him Because of his health condition So thank you for your prayers for him. He participated in a bible study last thursday night so I was teaching through zoom I had a bible study In guatemala and it was about sinners in the hands of angry god and so It was an appropriate study for For him and I was very thankful because normally he's not He doesn't participate in bible studies or like to come to church or So I was very thankful for him and it was all in spanish. So it was I think clear for him He's speaking english well, but it's even clear maybe in in his first language So those are some of the the difficulties in the church some of the difficulties Are working through covet issues trying to help people think through the importance of taking wise Calculated risks and saying yeah, you can't guarantee your health You can't guarantee your safety in driving to church either Can't guarantee your safety in many other things And so we don't take unwise risks We take calculated risks, but we still have to take risks in order to follow lord So trying to encourage people to have a bit a wise understanding of how we follow the lord and obey the lord and trust him and that we have to have a a Trust that leads us to having A valour or a brave to be brave in order to be able to do that in these times So it's the same thing in guatemala with by trying to encourage the people the same thing with we have the same issues with people afraid about those things and and some government overreach and their Their laws and we have a lot of the same difficulties there with covet and so We've also dealt with some members that seem to be moving on moving And it may be in churches as blend or it may be leaving The church with their members, but I'm not sure yet, but that's a process that's going on right now So that's some of the difficulties that are going on in the local church and in that particular Issue that's being worked through in the church with a potential church discipline is is really focused on not attending For a long time and not really participating It's not just not attending. It was not being part of the church body Really can't be a part of the church if you're not part of the church right So it's a it's a contradiction to say i'm a member but not attend and not communicate and not love and not serve as a member And obey the the basic parts of being a member So those are some of the difficulties that we've been going through And next slide, please brother So now we have the opportunity to be able to talk about some testimonies So I have some testimonies here And i'm not sure i'm able to get through a one or two to be able to Tell you a story We have a couple here Dennis and Janet Dennis and Janet are only been married about a year And the lord saved Dennis About four years ago in canada And the lord recently saved janet Just a few years ago as well, and they've been married. They're married just before covid began So i'm going to try and tell you Dennis's testimony Describing in a loose translation in his from his own his own words, okay So you can kind of look at him and listen to his own word as I describe him in a third person though So Dennis um Grew up in a christian background, but in actuality. He hated god He didn't hate god with clearly expressed in his words but more in his actions ever since he could remember his grandmother would take him to church And he always believed in the cross but never really understood the cross of jesus christ He was taught to repeat the sinner's prayer when he was convicted, but he never really truly understood true repentance Whenever he felt convicted about a sin, he would invite jesus to his heart again And whenever he felt that god wasn't with him, he would try and repeat the sinner's prayer But his life was full of conflicts and his family with his friends because of his pride His life was Folk was filled with self-love His idol was himself He would spend hours and hours and from the television addicted to video games He truly loved those things more than god He was prideful about how he could lie and deceive others And he would Congratulate himself on his skill in being able to do that He would constantly think that he was better than others He was full of bitterness with members of his family And had conflicts with them many conflicts with them He would constantly look at many evil things And delight in them and delight in sin He was completely lost without salvation Destined for the wrath of god and he decided To not think about god whenever he felt conviction in about these things or frustration or And he ignored the word of god He was in great need, but he didn't look for god and didn't know the glorious gospel of jesus christ All he knew was a mediocre gospel That left him feeling empty and miserable In the year 2012 God and his grace allowed him to move to canada In alberta canada A couple years after that in 2014 He began to hear online. He heard a video from john piper entitled you will suffer After hearing that video he began to think about his soul Began to attend pentecostal church And began to read the bible He could see some things and in the pentecostal church were not right But in the end he didn't think it was that important So as time went on later he heard a video from paul washer on the true gospel And he really did not like it He reacted sinfully He rejected what he heard he rejected the doctrines of grace and he felt very discouraged after being confronted And he didn't know exactly what to do and how to respond He felt lost from hearing this sermon And his life was a disaster My in the time of november of 2016 He once again heard another sermon from paul washer or the 10 indictments against the modern church And each word pierced him to the heart For the first time he understood The the biblical gospel what christ had done the cross of calvary How christ took his sins Upon him and suffered the wrath of god in his place And so like second corinthians chapter 5 verse 21 says That for he made him who knew no sin To be sin for us That we might become the righteousness of god in him Since that time god has been working in denises life transforming him To be more and more like jesus christ And in denises testimony he quotes The the same chapter verse 17 therefore if anyone is in christ he is a new creature Creation all old things have passed away behold all things have become new Dennis no longer feels the same joy and pleasure and sin that he once loved He began his life began to change Including the way he that he spoke to his parents And treated them which was much more respect And the way that he would treat others in general began to change He stopped laughing at sin He stopped swearing And he lost his desire to watch so much tv He instead prefers to read the bible and listen to biblical sermons And he stopped being so focused on himself and one began to be focused on the lord jesus christ And he wants to leave his pride behind Now he desires to be close to god the father god the son and god the holy spirit And give his life and service to lord Whenever he has the opportunity he desires to preach the gospel His co-workers his family his friends So thanks to the grace of god He's not the person that he was before amen Praise the lord for his work and the life of denise So i want to tell you another story of his wife janet so janet grew up in in guatemala in the countryside of guatemala and She grew up in a catholic home that was very dysfunctional And she grew up with a lot of hate in her heart Wrath and a thirst for vengeance against those who had hurt her And so all of this created many problems in her home Her father frequently abused her mother And and the the siblings and the family and when she would see this this really affected her She grew up hating and at the same time loving her father She grew up in a nominal catholic home But she really doubted a lot of the things that they did the worship through the use of images and she Didn't really consider herself a genuine catholic But through all this anger and bitterness of growing up this way in the home She would often have the desire to take her own life out of the frustration and desperation Of living in a home like that She knew that god existed But she really didn't look for god One night she had the opportunity to go to an evangelistic campaign or evangelistic rally And the people in the pentacolster church preached a revelation 320 About god christ knocking at the door of your heart And so looking for hope She walked the isle And repeated the the sinner's prayer and asked jesus into her heart And she thought this would be the solution to her problems If she repeated this prayer About the problems continues the years went by and as she went to the to the pentacolster church now She began to try and find the solution in more rigorous good works So she would often fast pray and participate in all night prayer vigils To and hoping that through these all night prayer vigils god would give her what she wanted They never really preached about sin in this church And the church is that she was in a um in a oneness pentacosal church. So if you know td jakes and uh it They deny that the trinity and they also teach a workspace salvation And so they Baptized her teaching that she couldn't be saved until she was baptized And that she couldn't go to heaven without receiving the back what they called the baptism of the holy spirit And so this all led to her Having a constant worry about her soul and having no security of salvation In 2016 she met her husband And she began to understand through him Many of the things that she had doubts about in the pentacolster church And she learned about how to dance and dancing in the spirit speaking in tongues And slaying people in the spirit was is all and not biblical He helped her understand that you should not supposed to Yell when you pray and if you've been in those circles, so maybe you understand some of those things And he began to introduce her to preaching from paul washer And so through the sermons she began to see the difference between the true gospel and the false gospel And understand the false teachings of the the oneness pentacosalism She began to learn the doctrines of grace sound doctrine And she learned that her salvation was not based on what she could do but what christ did on the cross And god in his sovereign mercy helped her to understand who christ was Who she was in her sin That christ was sent by god the father to take all the wrath that she deserves And suffered in her place Washing her of all her sin And god her sovereign creator gave her the faith and the ability to Trust in christ as her savior and lord Even though she didn't she knows she deserves god's wrath as a miserable sinner She rejoices in god the salvation that christ has offered She began to confront the church where she was at when she would begin to learn more of the the gospel And to be generally converted But they responded by Not allowing her to attend They have a phrase about taking away privileges That's a common You don't have privileges in the churches of common pentacosal way To uh, it's like a half discipline. It's kind of a weird thing But maybe some of you kind of understand that better than me experientially even and so they no longer considered her to be a christian and But she knows that the lord has saved her And allowed her to know more of him and to serve him to worship him And to give her life in his service She doesn't have the same hatred and bitterness and thirst for vengeance that she once had And now she's learning to pray to god and depend upon him In those times of of difficulty and learning to grow in the struggle to trust the lord And so she's certain of god's work in her life And she's forgetting her past life each more and more daily and learning to grow in forgiveness and so We we're just going to be able to give two testimonies today in the update that Hopefully you guys are are receiving emails and updates. There's another testimony. That's if you could switch the slide brother There's an another family And there's a testimony of a brother named Juan On the left that's very clear very encouraging and I hope you're getting those email updates If you're not, please talk to my wife Just give her a piece of paper with your email and she can add your email to and also we hope to be able to have those updates on the app In time But there's a very encouraging clear testimony I have I would like to be able to someday tell you His wife's testimony as well, but for a different time so Those are some of the things the lord has been doing in the past four months We tell those testimonies because they were uh These are new members of the church and since that we've last visited you they've Been baptized And our members of iglesia and torcha So what's coming up in this next month? We're gonna Have a missionary team coming from cornerstone To be able to preach in a mini conference and ryan's going to lead that trip And we're excited about that We're going to hopefully finish the book of abacus Within a few weeks, maybe hopefully seven weeks or so And then we're going to begin the book of genesis. We should be a nice long study We're also going to study pilgrim's progress this year So I hope that that would be edifying for the the church If you would like to continue to pray for us and continue to know what's going on Please connect with my wife be able to lay in the back with her hand up Give her your email so that you can receive those updates So ways to pray for us Please praise god for his saving work praise god for adding to his church Please pray for god to raise up future leaders in the church And future pastors to serve with me Please pray that god will raise up future church plants People are traveling from Four hours to three hours various families So We really need church plants in these various places So part of the trip the next few weeks is to visit one of those cities A few hours out and evangelize there and we pray that that would be Perhaps the beginning of a church plan And so please pray that that god will give us the grace to persevere in the spiritual war Like we talked about in Ephesians 6 Okay, so I talked a little too long guys. Sorry if you have questions I'm gonna be available all day. So you can ask me questions In person. Okay. Let's go ahead and pray Lord god, we want to thank you and praise you for the great things you're doing Thank you for being at work and your true churches all over the world Thank you that we can be have lives focused on you And glorifying you and not lives focused on selfishness And our own desires. Thank you for saving us from our own idolatry Thank you for leading us to worship you and Giving us to count our hearts of stone giving us hearts of flesh and Eyes to see and understand the gospel and trust in you repent of our sins Thank you lord for doing that in our in iglesia and torcha. Thank you for doing that here Thank you for giving us this day to worship you So, please be glorified in your worship service. Amen


Fonts, let's talk some more about fonts. Most designers will use a number of different fonts when they are designing a website, but will also reuse the same font using different weights, widths, or slants. On the web, that usually means downloading an additional font file per configuration, and that can add up to a few hundred kilobytes quite quickly. And this is where variable fonts come into play. With variable fonts, you can change certain settings of a font without having to load a new font file. So for example, using the gingham font, I can change both the weight and the width of the font using the font variation settings attribute. Some settings that is width and weight have standardized abbreviations that I'm using here, but fonts can expose an arbitrary number of settings for you to change. While it should be used with care, you can even animate these settings to transition between different font layouts. Keep in mind, though, that this will cause the browser to re-layout and repaint, which will become quite expensive really, really quickly. Bye. I've been continuing Serma's analysis, and a new graph just came in. If you prefer the yellow line, you should be subscribing to this channel. If you prefer the green line, you should be watching the latest Supercharged video. But really, these lines mean nothing. You should just be doing both.