XS sent us two pairs of headsets and we've been using it for quite some time now. Good pair ba sila for music? Is the mic performing well on comms or conference? Will it give you more frags? Anjay the tech guy and in this video we're gonna be reviewing XS E910 and E1000. Here we go. Hindi niligan ng DC. Bustay di kailaw na windows. Pero san ko hupuwan ng digit windows? Daming options, daming prices. Akali ko. Gudi na lang. May cdkovers.com. Wadalilaw ang order. Search for the software you need. Add to cart. Dahan ka sa payment options nila. Wala pag 5 minutes. Finished. May legit, working cdk ka na. Para sa windows mo. Gamitan ng aming code para makakuhapan ng discounts. Kaya kung nagahalap ka ng legit, mura at original software. Check out cdkovers.com. XS E910 is using a 5.8 GHz connection. 5 GHz meaning lower yun latency niya pero may klilang din yung coverage. Compare dun sa usual 2.4 GHz headsets, meron siyang latency but greater yung range. I like how they went with 5 GHz connection instead of keeping it at 2.4 GHz. Kasi you're not really going away from your PC. Unlike Wi-Fi where we always see this bandwidth, kailangan niya ng greater range to cover your area. Stabilizing the connection of your headset is seamless. Ipaplag mo lang yung USB dongle niya and outright mag-install na yung drivers yung headset. Compare dun sa other brands, usual brands na kailang mo pang install yung software nila i-update yung firmware before mo magamit yung headset. With 1200mAh battery, charging it will usually take 2 hours and can last up to 10 hours with 70% volume. Nag-charge ako around 2 hours in on average usage na lobat sa after 3 days. E910 has leather cushions. They're thick and soft at the same time but it's causing me discomfort as the head clamp is too tight for me. If you have a big head like me, maybe you'll feel the same way. It has 10 settings sa piece, both left and right so you can align the ear piece or the drivers based on your preference. This pair is using the usual 50mm sound drivers. It has 2 modes, stereo and 7.1 virtual surround. You can switch them by pressing the on and off switch once. Yan kaw naririnig niya. To yan, to switch from stereo to virtual surround or the vice versa. 7.1 virtual surround sound nimimik niya yung parang marami kang speakers around you. Yun yung intended na feel. Ok sa on music, maganda yung feel. Clear yung bass, define yung bass. For E910's mic, there are parts na medyo. Sharp yung the thing and static noises from the background can be picked up even if the mic's ENC feature and excess software is enabled. Mic is retractable and the quality is ok comparing to the other brands in the same price range. Pero on gaming, it feels like the sound pure sound source is a lot more near or kung saan hindi mo sila inee-expect. Like sa valoran, say for example feeling mo malapit na yung footsteps pero hindi pa pala talaga. Na sa corner ka, inee-expect mo na magpapas na siya pero hindi pa pala, malayo pa pa siya. Ya, it feels like that. So if you're gaming, I would suggest na use the default stereo mode kasi it's a lot more accurate compared dun sa 7.1 surround sound. The headband feels pretty sturdy. I stretch it on every way possible. Plastic on the earpiece feels premium and has a mesh design na may red triangle LED. Has volume scroll wheel, mute button. Type-C port for charging on and off switch at the left earpiece. Nothing much on the aesthetics but that's what I like about it. It doesn't shout its brand like other peripheral manufacturer na sobrang ako'y na sa branding nila. So minor gripes, I think a longer USB type-C cable should be added as the included USB type-C cable is a bit short so you cannot use it while charging. Now with Exa E1000, it uses the usual 50mm drivers. It has a 2.1 meter braided USB cable. Controls are in the cable and it also uses surround sound. The clamp is pretty strong. Di mo'y iisipin na malalaglag sa agad but that's what also makes me ang comfortable. This might be a personal preference but if you have a big head like me, you'll have to take breaks after wearing it after an hour or two. Usual leather cushions na may kita mo on headsets in this price range, they're pretty decent and I have nothing to complain about it. O'y siya for music from what it is but for gaming, hindi na off yung surround sound so yung gripes ko earlier within 910, hindi siya nawawa wala dito. The E1000's mic is okay as you can hear malino naman yung recording niya. Yun nyalang walang noise cancellation yung mic so malawak yung threshold niya to pick up noise from the background. All in all, decent mic for its price. Like in 910, I stretch it to every way possible. Plastic feels sturdy, hindi siya magsasnap up easily. No? Diba? Volume and mic controls are in the wire so hindi mo nakilangan kapayin sa earpiece as a foldable mic na hindi mo makikita in headsets within this price range. Has a RGB logo na merong static na RGB border. I'm giving four kendis for E910. It's a good pair but it can still do better comparing to the other brands within this price range. Do naman sa E1000, I'm giving it 3.5 kendis kasi you're getting what you pay for but you're not paying a lot. Sir, not getting a lot. Standard disclaimer, Exa sent us these pairs but they have no say on what we have to say or what is our verdict in this review. If you like this video, hit like, subscribe if you haven't already. If you have other headphones, and recommend within this price range, please comment it down below and see you next video. Pamin saan may nagtatanong kumikilala ba kaming computer shop na trusted yung hindi kalolo ko hin? Actually meron kaming Full service PC store ang hardware sugar. Nagbabenta kami ng PC components. Nagbabenta rin kami ng fully assembled rigs. We clean computers. Kasama na rin yung excellent cable management namin and CPU cooler repasting sa cleaning. We also clean and repaste GPUs. Nasamakati yung physical store namin and you can also buy from our site www.hwsugar.ph na 100% palaging up-to-date yung inventory dun. Kung instock yung item sa amin, available yung sa site. We also ship nationwide. Thanks for watching and maybe one of these days, magkita tayo sa shop.


Number two, don't force the relationship. I'm here to say, I want you to think of a relationship like a ping pong game. You're mutually making effort to one another. You're driving down a two lane street side by side. It's not you pulling him along. If you have to pull a man along, in other words, if you have to constantly send text message to say, hey, I'm here, you know, then it's probably not the right relationship for you. It's probably not the right man for you if you have to force or push the relationship along. It should be a nice gradual giving and receiving.


So, we are considering Gaussian integration. Last time, what we have done is we looked at three functions f x is equal to 1, then f x is equal to x and f x is equal to x square for x belonging to interval minus 1 to 1. Then using Gram-Schmidt orthonormalization process, we constructed three orthonormal functions. The third orthonormal function, which is the quadratic function, it is perpendicular to any linear polynomial. This quadratic function, it has got two distinct roots. So, those are known as the Gauss points and then based on that, we fit a polynomial of degree less than or equal to 1 integrate. So, that is our Gaussian integration. So, today we are going to find a formula for these Gaussian integration based on these two points. So, we will be doing it first for the interval minus 1 to 1. We will also find the error in this interval minus 1 to 1. Then using the result on interval minus 1 to 1, we will look at interval a b, general interval a b. After that, we will consider composite Gauss two point rule and then we are going to prove the convergence of Gaussian quadrature. That means, first we are looking at Gaussian integration based on two points. So, we will define the general Gaussian quadrature based on say n plus 1 points and we are going to prove convergence of the numerical quadrature method. So, let us look at the what we did last time. So, our functions were f 0 x is equal to 1 constant function, f 1 x is equal to x and f 2 x is equal to x square on interval minus 1 to 1. From these three functions, we constructed g 0 x to be 1 by root 2, again a constant polynomial, g 1 x to be root 3 by 2 x, a linear polynomial and g 1 x to be root g 2 x to be x square minus 1 third multiplied by this constant. The constant is the normalization factor which makes norm of g 2 to be equal to 1. So, this function g 2, it is perpendicular to constant polynomial g 0, it is also perpendicular to linear polynomial g 1. Then look at x square minus 1 third. So, that is factorized as x plus 1 by root 3 x minus 1 by root 3, because g 2 is perpendicular to the constant polynomial, we get integral minus 1 to 1 x plus 1 by root 3 x minus 1 by root 3 d x is equal to 0 and because g 2 is perpendicular to g 1, we get integral minus 1 to 1 x plus 1 by root 3 x minus 1 by root 3 x d x is equal to 0. So, last time we had seen that when we want to find a numerical quadrature formula of the type w 0 f of x 0 plus w 1 f of x 1, if we want this to be exact for polynomials of degree less than or equal to 3, then our points x 0 and x 1 should be so chosen that integral a to b x minus x 0 x minus x 1 d x is 0 and integral a to b x minus x 0 x minus x 1 x d x is equal to 0. So, this fact now we have achieved on the interval minus 1 to 1. So, our x 0 is going to be minus 1 by root 3 x 1 is going to be plus 1 by root 3. We are going to fit a linear polynomial which is based on interpolation points x 0 and x 1 which is minus 1 by root 3 1 by root 3. We will integrate and we will get a approximate formula and then we will look at the error. Now, let us look at the polynomial f x 0 plus divided difference based on x 0 x 1 into x minus x 0. This is the interpolating polynomial and this is the error divided difference based on x 0 x 1 x x minus x 0 x minus x 1. Let us integrate between minus 1 to 1 f x d x. So, it is integration of f x 0 plus divided difference based on x 0 x 1 into x minus x 0 d x which will be the first term will be give us 2 f x 0. The divided difference f x 0 x 1 is f x 1 minus f x 0 divided by x 1 minus x 0 x minus x 0 square by 2. Evaluate it between minus 1 to 1. Then the integration when you put 1 and minus 1 that will give us the term 1 minus x 0 square by 2 minus minus 1 minus x 0 square by 2. Use the fact that x 1 minus x 0 is going to be 2 by root 3 and that is equal to minus 2 x 0. When you expand this you are going to get minus 2 x 0 then from here also minus 2 x 0 and then divided by 2. So, that is minus 2 x 0 that will get cancelled with x 1 minus x 0 and that gives us f x 0 plus f x 1. Next let us look at the error. So, error has f of x 0 x 1 x multiplied by our function w x d x integral minus 1 to 1. So, as we had done before we will use recurrence relation for the divided difference f x 0 x 1 x. You cannot take out f of x 0 x 1 x as such, but when using recurrence relation we write it as f of say y 0 x 0 x 1 plus some term. Then f of y 0 x 0 x 1 that being a constant it will come out of the integration psi and then we use the fact that our x 0 and x 1 these are some special points. So, using those properties we are going to get our error to be based on divided difference of f with x 0 repeated twice x 1 repeated twice and then some point c and then integral minus 1 to 1 x minus x 0 square x minus x 1 square d x. In order to have this term we will be using the mean value theorem for integral and that will give us a error bound. So, this is our expression for the error we have got integral minus 1 to 1 x minus x 0 x minus x 1 d x is 0 also integral minus 1 to 1 x minus x 0 x minus x 1 x d x is equal to 0. This since it depends on x I cannot take it out of integration, but using the recurrence relation for divided difference we write it as f x 0 x 1 x is equal to f x 0 x 0 x 1 plus divided difference based on x 0 x 0 x 1 x into x minus x 0. You can take this term on the other side and divide by x minus x 0. So, that is the divided difference formula for f of x 0 x 0 x 1 x. Now, again for this divided difference we use a similar formula. So, this is the divided difference we write as it is f of x 0 x 0 x 1 plus you have divided difference based on x 0 x 0 x 1 x 1. So, I am introducing point x 1 multiplied by x minus x 0 plus the term divided difference based on x 0 repeated twice x 1 repeated twice and x multiplied by now we have introduced x 1. So, that is why you have x minus x 0 into x minus x 1. So, this we have obtained using the recurrence formula for divided difference. This expression we will substitute in our error. So, when I substitute this term there is no dependence on x. So, it will come out of the integration sign integral minus 1 to 1 x minus x 0 x minus x 1 d x is 0. So, no contribution from here again this divided difference is independent of x. So, it will come out of the integration sign and you will have x minus x 0 x minus x 0 x minus x 1 d x. Then using these two relations the contribution from this term also will be 0 and you are left with integral minus 1 to 1 the divided difference based on x 0 repeated twice x 1 repeated twice x you will have got x minus x 0 x minus x 1 and here you had x minus x 0 x minus x 1. So, you get x minus x 0 square x minus x 1 square d x. So, this is the error term. Now, in this error term our divided difference is going to be a continuous function provided our function is sufficiently differentiable. We have got our divided difference based on x 0 repeated twice x 1 repeated twice and x and x can take all the values. So, it can take value x 0 it can take value x 1. So, in order that such a divided difference should be defined we will need the function to be three times differentiable. Look at the term x minus x 0 square x minus x 1 square this term is going to be bigger than or equal to 0. So, we have got two functions one function is continuous other function is bigger than or equal to 0 and hence the mean value theorem for integrals it is going to be applicable. So, using the mean value theorem we take out the divided difference term out of the integration as divided difference based on x 0 repeated twice x 1 repeated twice and some point c and then what remains is integral a to b x minus x 0 square x minus x 1 square and then d a. Now, recall our x 0 is minus 1 by root 3 x 1 is plus 1 by root 3. So, when you consider x minus x 0 into x minus x 1 that is x square minus one third we have got x minus x 0 square x minus x 1 square. So, that is going to be x square minus one third whole square and that is something you can integrate between minus 1 to 1 which is what we will do in order to get a formula for the error. Also, the divided difference which is based on five points if our function f is four times differentiable then that divided difference we can write as equal to fourth derivative evaluated at some other point say d divided by four factorial. So, that gives us the error in this Gaussian rule based on two points minus 1 by root 3 2 plus 1 by root 3. So, the integration of minus 1 to 1 x square minus one third whole square d x you will have term x raise to 4. So, its integral will be x raise to 5 by 5 then you have minus 2 by 3 x square that in its integration will be minus 2 by 9 x cube plus 1 by 9 its integration is going to be x. The divided difference we are writing as at f 4 d upon four factorial where d is some point in the interval minus 1 to 1 then you simplify this put 1 and then we put minus by the value obtained by putting minus 1 here. So, that value you can check that it comes out to be 8 by 45 and that gives you the error to be f 4 d divided by 135 and thus the Gauss two point rule is going to be integral minus 1 to 1 f x d x is approximately equal to f of minus 1 by root 3 plus f of 1 by root 3 and the error is going to be f 4 d divided by 135. Now, look at the error term the error term contains the fourth derivative of the function. So, if the fourth derivative is identically 0 which is the case if our function is a cubic polynomial then the error is going to be 0. So, we have got only two function evaluations and then the formula is exact for cubic polynomials. When we had looked at the trapezoidal rule there also we had only two interpolation points the interpolation points where end points point a and point b and in that case the formula was exact for polynomials of degree less than or equal to 1. So, this is the advantage of Gaussian rules. Now, this formula is valid on the interval minus 1 to 1 we want to derive a formula on the interval a to b a general interval. So, what we are going to do is we are going to look at a 1 to 1 on to map from the interval minus 1 to 1 to interval a b and then we will be looking at integral a to b f x d x. So, if you have a map phi from the interval minus 1 to a b then we will do the change of variable formula and then obtain Gauss 2 point rule on a general interval a b and we will also look at the error term in this case our error term is f 4 d divided by 135. When we look at the interval a b then there will be b minus a coming into picture. So, you will have the power of b minus a raise to 5 and then some constant. So, let us now look at 1 to 1 on to a fine map from interval minus 1 to 1 to a general interval a b. This map is given by t plus 1 into b plus 1 minus t into a divided by 2. So, the domain of a is equal to a plus b by 2 plus t into b minus a by 2. So, first of all notice that when t is equal to minus 1 in that case this term will vanish and you will get phi of minus 1 to be equal to a. When you put t is equal to plus 1 no contribution from 1 minus 1 minus t into a. So, you are going to have b then the derivative of phi that is equal to b minus a by 2. So, phi dash of t is going to be strictly bigger than 0 that means phi is a strictly increasing function. So, we have a map from minus 1 taking going to a 1 going to b and it is strictly increasing. So, that is why the range of our phi is going to be closed interval a b which proves that such a map is on to phi dash t bigger than 0 that means it is strictly increasing and hence it is going to be 1 to 1 and it is called a fine because it is of this form. When if you had no constant only t times something that is known as a linear map and this will be a fine map. So, we have got phi double dash t to be equal to 0. So, thus we have 1 to 1 on to map from the interval minus 1 to 1 to interval a b. Now look at integral a to b f x d x, x is varying in the interval a to b. Any point in the interval a b is going to be phi of t for some t in the interval minus 1 to 1. So, we will put x is equal to phi t then d x by d t is going to be phi dash t. So, that phi dash t is b minus a by 2. So, our integration a to b f x d x we will replace it by integration over minus 1 to 1 of the composite map f composed with phi of t and then on minus 1 to 1 we have got our formula for Gauss 2 point integration. Look at integral a to b g x d x that will be equal to integral minus 1 to 1 g of phi t phi dash t d t and this is equal to phi dash t we have seen that it is b minus a by 2. So, it comes out of the integration sign and it is integral minus 1 to 1 f t d t where f is the composite map g composed with phi.  So, it should be actually g it should be g of phi of minus 1 by root 3 plus g of phi of 1 by root 3 and then the error is going to be b minus a by 2 minus f 4 d divided by 135 look at our Gauss points in the interval minus 1 to 1 the Gauss points where minus 1 by root 3 and 1 by root 3. Then we look at our affine map phi and image of minus 1 by root 3 and 1 by root 3 by this affine map those are going to be Gauss points in the interval a b in the interval minus 1 to 1 the Gauss points minus 1 by root 3 and plus 1 by root 3 they are symmetric about the origin 0. So, 0 was the midpoint of the interval minus 1 to 1. Now, here in the interval a b the Gauss points they are going to be symmetric about the midpoint a plus b by 2 look at our error. Error has got 1 term b minus a by 2 and then fourth derivative of the function that function is f and our f was g composed with phi. So, our g is the function which we are trying to integrate over the interval a b. So, we will like to have the error formula in terms of the derivatives of g. So, this f 4 of d fourth derivative that is going to be g composed with phi its fourth derivative. So, we will use chain rule and then obtain a formula in terms of the derivative of g. So, when we do that in the process we will get powers of b minus a. So, let us do that now. So, this is the error f 4 d upon 135 b minus a by 2 our function f of t is g composed with phi t. So, we use the chain rule. So, the chain rule is f dash of t is equal to g dash of phi t into phi dash t phi dash t is b minus a. So, we get g dash phi t. So, that is the first derivative. Now, look at the second derivative f double dash phi t f double dash at t that will be g double dash phi t and then phi dash t square because we have got here we are differentiating this. So, it will be g double dash phi t into phi dash t square and then we can have g dash phi t and then the derivative of phi dash, but phi double dash t is 0. So, that is why we have got only g double dash phi t and then phi dash t being b minus a it is b minus a by 2 square. When we look at the third derivative f triple dash t that is going to be equal to g triple dash phi t one more b minus a by 2. So, you will get b minus a by 2 cube and then fourth derivative will be fourth derivative of g at phi t b minus a by 2 raise to 4 and hence the error is fourth derivative of g evaluated at some point phi d in the interval a b divided by 135 and then b minus a by 2 raise to 5 and the Gauss two point rule for the interval a b is b minus a by 2 into f by 2.  So, x 0 and x 1 they are symmetric about the midpoint. The error is fourth derivative evaluated at some point divided by 135 into b minus a by 2 raise to 5. So, we have got only two function evaluations the formula is of the type w 0 f x 0 plus w 1 f x 1 the weight w 0 is equal to w 1 is equal to b minus a by 2 and x 0 and x 1 these are the Gauss points. So, now we have found a basic Gauss two point rule and what we did for the trapezoidal rule Simpson's rule midpoint rule etcetera we considered composite rules. That means, we divided our interval a b into sub intervals of equal length on each interval we applied our basic rule and we added up the result to get integral a to b f x d a. So, now, same thing we are going to do for Gauss two point rule in case of composite rules which we have studied earlier we saw that if you have the b minus a raise to k in the error formula for the basic rule then when you add it up then from each sub interval the contribution is some constant times h raise to k where h is the length of the sub interval. We are adding n such terms and our h is b minus a by n. So, we associate with one h with such a sum of n quantities and then we will get a constant, but in the process we have lost one power of h that cannot be helped in the composite rule that is going to happen. So, here for our Gauss two point rule when we will apply to say interval t i to t i plus 1 of length h then we are going to have a term h by 2 raise to 5 in the basic rule we have b minus a by 2 raise to 5. So, now, it will be h by 2 raise to 5 and 1 h will get lost. So, our composite Gauss two point rule will have the order of convergence to be equal to h raise to 4. Now, this type of argument we have used before. So, I will be quickly going through the argument and showing that in the composite Gauss two point rule our order of convergence is going to be h raise to 4. So, the interval a b consider its uniform partition each sub interval t i to t i plus 1 will be of length h which is b minus a by n. In order to find the Gauss two points in the interval t i to t i plus 1 we have to look at a fine map from minus 1 to 1 that I denote by phi i and value of phi i at t will be given by the midpoint t i plus t i plus 1 by 2 plus t times earlier we had b minus a by 2. So, now, it is going to be t i plus 1 minus t i divided by 2. So, this is nothing but h by 2 then in each interval we are going to have two Gauss points the Gauss two points in the interval t i to t i plus 1 we denote by u 2 i plus 1 which is image of minus 1 by root 3 by this a fine map phi i and u 2 i plus 2 which is image of 1 by root 3 by the same map phi i. So, thus our two Gauss two points in the interval t i to t i plus 1 they are given by the midpoint of the interval minus t i plus 1 minus t i being h minus h by 2 root 3 and t i plus t i plus 1 by 2 plus h by 2 root 3 and i is going to vary from 0 1 up to n minus 1 this n should be n minus 1. So, you are going to have in all two n Gauss points next integral a to b f x d x we split it as integral t i to t i plus 1 f x d x i going from 0 to n minus 1 which is approximately equal to summation i goes from 0 to n minus 1 h by 2 that was our b minus a by 2 that was our b minus a by 2 value of f at u 2 i plus 1 plus value of f at u 2 i plus 2 these are the Gauss two points in the interval t i to t i plus 1 when we look at the error it will be summation i goes from 0 to n minus 1 f 4 d i by 1 35 h by 2 raise to 5 assuming the fourth derivative of f to be continuous we can replace summation i goes from 0 to n minus 1 f 4 d i divided by n by f 4 eta h is b minus a by n. So, that 1 v that n we associate to get f 4 eta. So, we have got b minus a it was h by 2. So, that is why this 135 becomes 270 and 1 h by 2 is gone. So, we have got h by 2 raise to 4. Now, compare this with the composite Simpson's rule in case of Simpson's rule we had got three interpolation points the interpolation points where two end points and the midpoint we fit a parabola. So, as such we expect that the error should be 0 for quadratic polynomial, but it is the property of even degree interpolation that if your interpolation points are chosen symmetrically in that case you get one extra degree of exactness. That means, we expect that there should not be any error for quadratic polynomial, but there is also no error for cubic polynomial. So, for Simpson's rule we achieve the exactitude for cubic polynomials with three points for Gaussian quadrature with two points we achieve that there is no error for cubic polynomials with two points. Now, in each interval we have got two Gauss points. So, total there are two end Gauss points for the Simpson's rule in each interval we have got three points but the two end points are included in the Simpson's point. In case of Gaussian quadrature both the interpolation points those are the interior points in the interval ti to ti plus 1. So, in Simpson's rule because the end points are interpolation points they will be common to the adjoining interval and hence the total number of points which will come into picture for the composite Simpson's rule they are going to be 2 n plus 1 and for Gaussian point we have got 2 n. So, then there is an difference between 2 n and 2 n plus 1 because when you look at the value of n to be large then 2 n and 2 n plus 1 they are considered as the same. So, that means the Simpson's rule and the Gauss 2 point rule they are going to be on par when we compare the order of convergence and the number of function evaluations when we compare two rules that is generally our criteria. How many number of times I need to evaluate the function and then what is the order of convergence and then we saw that in the corrected trapezoidal rule we need also the derivative values. So, that becomes an additional say a criteria. So, whether you need to evaluate only functions or whether you need the derivative values how many function evaluations and the order of convergence. So, based on these criteria the Simpson's rule and Gauss 2 point rules they are going to be on par. Suppose our function if it is continuous as I had remarked in the last lecture that the differentiability properties of function they are assumed for obtaining orders of convergence, but if I am interested only in knowing whether there is a convergence or not. Then in that case we may not need the differentiability like in case of say either composite rectangle rule or composite midpoint rule we saw that our rule is nothing but a Riemann sum and hence we had continuity. Hence we had convergence for continuous function same was the case for trapezoidal rule it is the sum of two we can write trapezoidal rule as a two Riemann sums both of which converge to integral a to b f x dx and then we are dividing by 2. In Simpson's rule also similar thing can be done in all these cases so far what we were doing was we were fixing degree of polynomial and then applying it to small intervals. Now, for the Gaussian rule whether we can increase the degree of the polynomial that means we have found Gauss two points. So, whether there are Gauss three points Gauss four points and so on. So, you increase the degree of the polynomial. So, our method has been replace the function by interpolating polynomial we know how to integrate a polynomial get a numerical quadrature rule and we have no ruled or we do not have a set of interpolation point which guarantee convergence of interpolation polynomials for all continuous functions. Now, the Gauss two points rule like we are going to define what are the Gauss points like we have defined Gauss two points like that we are going to define Gauss k points. So, now we have got a set of rules like for any n we can specify n Gauss points you fit a polynomial. Now, this set of interpolating polynomials will not converge to the given function in the maximum norm for all continuous functions that is not possible. But what we are going to show is even though the interpolating polynomials may not converge our numerical quadrature is going to converge and so on. And in that what the important point is that the weights in the Gauss points they are going to be bigger than 0. So, that is what we are going to show we are going to show that the Gaussian integration it converges for all continuous function just the assumption is that the function f should be continuous. So, for that now we have to first define what are the Gauss points the Gauss two points they were obtained as roots of certain quadratic polynomial and that quadratic polynomial was perpendicular to one and constant polynomial and the polynomial x. So, instead of applying the Gram-Schmidt orthonormalization process to three functions 1 x x square we can apply it to n functions obtain orthonormal polynomial and then look at the roots of such appropriate orthonormal and then look at the roots of such appropriate polynomial those are going to be our Gauss points. So, those are the known as Legendre polynomials. So, recall that x is C a b vector space of continuous functions defined on interval a b taking real values we define inner product f comma g to be integral a to b f x g x d x norm f 2 is the induced norm from this inner product.  So, it is the same process we had considered before where we had looked at 3 functions f 0 f 1 f 2. Now, we are looking at a infinite set and then we construct such polynomials and then we will see these are known as Legendre polynomials and the 0s of g k they are known as the Gauss points. So, we will show that these polynomials which we construct g k is going to be a polynomial of degree k. So, it is going to have k roots, but what is important is it is going to have k distinct roots those roots or those 0s those are known as the Gauss points and those are going to be our interpolation points for fitting a polynomial of degree less than or equal to k minus 1. Now, because of the orthogonality property our g k is going to be a polynomial of degree k and it is going to be perpendicular to functions 1 x x raise to k minus 1. So, that means our g k is going to be perpendicular to any polynomial of degree less than or equal to k minus 1. As I said g k is going to have k distinct roots. So, I can factorize it and I can write g k x as x minus x 0 into x minus x 1 into x minus x k minus 1 and then multiplied by some constant the leading term. So, the orthogonality property of g k 2 functions 1 x x raise to k minus 1 that means if I look at integral a to b x minus x 0 into x minus x k, if I multiply by constant function 1 and take the integral that will be 0, if I multiply by x and take the integral that is going to be 0 and so on. So, that is the property of interpolation points allows us to obtain exactitude for higher degree polynomial. So, that is what we are going to do next time and then. So, we will we are going to define these Gauss points or we have defined Gauss points we consider Gauss Gaussian integration then in the Gaussian integration we will show that the weights. So, the Gaussian integration formula is of the type summation w i f x i i goes from 0 to n then these weights we will show that they are bigger than 0 and using that we are going to prove the convergence of Gaussian root. So, we are going to do this and then we are going to consider some problems next time. So, thank you.


And I sold these right here, these little mini racers. They're from Plains. Can you see how they have the marble in them?  Hey, Bolo buddies, thanks for watching. Amazing, right? All right, let's get started. All right, Bolo buddies, we are back with part two. Thanks for being here, thanks for hanging out. The video was too long, so I chopped it in half and I'm gonna release one in the morning and one tonight. You do not have to watch these in order, but definitely go check out part one. This is a reseller vlog. Basically in this video, I'm gonna tell you items that I sold, we're gonna pull them. I'm gonna share with you where I got it, what I paid for it and what it sold for.  So let's stay tuned for the rest of that bag also. Thanks for being here and thanks for watching and be sure to subscribe. Okay, here's my friend. Toad, is it Toad 23? I already forgot. This item came from the Benz Bingo Challenge and if you guys watched that video of mine. These items were gifted to me from a viewer. Check out her link down in the description of the video that I see. I'd probably have to look a little deeper. Here's a little elf. This will be cute for Christmas, get that listed. This one is by Fiesta. Cute, I've got this little teddy. This one looks vintage. It is made by Cuttlewit. Another little reindeer small plush. Kind of reminds me of like a beanie baby style hug and love, hug and love. So it was a doll that I had to use Google Lens to look up because I was not familiar with it and she actually sold pretty quickly. She is Masha the Bear, I think, from that movie or show or something, I don't know. But she sold for $21 free shipping on Mercari. So again, I cross-posed from eBay to Mercari and Poshmark and this little gal sold quicker on Mercari. I use this perfectly. You guys have heard me talk about it before. There's a link down in the description with a video attached that will show you how to use LIST perfectly. And if you use my code to join, you can get 30% off your first month. So check that out down below. I picked up these new boxes and they're seven by five by three and the reason I did it is because I feel like I always have, they're always too wide and I feel like this right here is better for something like this. But here's my problem. Let me put it together and I'll show you. I just don't feel like they seal like very nice. Like they're wonky. Like they're wonky. It bugs me, it bugs me. But I am gonna put her in some bubble wrap, sit her down in there like that and that's how I'm gonna ship her. But I am gonna bubble wrap her just to protect her plastic, the skin and keep it from getting damaged during shipment. So I could probably just put her in a piece of tissue but we're gonna use bubble wrap. All right, so you can just kind of see like I just want it to be all crisp and even and it's not. But I do like this size. So, yeah. That's another thing you guys might not know about. You can get priority mail stickers. So let's say you use your own packaging or box because you don't have the right size priority mail box. You could just slap one of these stickers on. I do think that you have to actually call the USPS.com number, the phone number and ask them to mail you a roll if I remember correctly. I've had these for a while. Me and their date of 2014. So I think I had to call to get these. They may be on the website, not 100% sure but they will send it to you free of charge. Right, we're in tote eight and I sold these right here. These little mini racers, they're from Plains. Can you see how they have the marble in them?  So for 40, let me go get the exact total for you. And the buyer paid shipping and tax on those. So I'll get you the exact total here in a minute. All right, I just checked $46.50 plus shipping. Okay, we are heading over to tote 30 and I have a replacement part that sold. We're gonna have some fun looking these up because I don't know what a lot of these are. This one is made by Hallmark cards which I like selling stuff by Hallmark. And it's a cute little reindeer. How cute is that? Be good for Christmas. Look at that, is that a raccoon? It is made by Animal Jam, cool, 2016. I know that Animal Jam makes little toy figures. Here is an elf on the shelf I think. No, is it? Is it? I don't know. I know if it's not actually elf on the shelf, do not put elf on the shelf because it will get taken down by eBay. A lot of people were, for the little knee huggers, the vintage ones, they were putting elf on the shelf and they were getting removed. So you definitely don't wanna do that. I'm not sure what brand this is. So I will probably, I'm guessing, I thought maybe it had, looks like the knees can fold up on it. But I don't know, I'll have to look that one up. It looks kind of like the elf on the shelf, but bigger. This also came from the Goodwill Benz. I ripped these off a dollhouse. It was a Barbie dollhouse. The dollhouse was in horrible condition. It was going to the dump. So I took a door and I took the windows off and I saved them. Somebody needs these. They're gonna replace their broken ones with these. So instead of them going to the dump, I will sell replacements. So if you ever see me at the Goodwill Benz and my Goodwill Benz videos, ripping doors and stuff off of the houses, the house is typically damaged or it's been sitting in a bin and nobody is gonna take that house and it's gonna go to the dump. So I had somebody give me a hard time about it once, but I saved it. I saved it. These replacement windows sold for $20. The buyer was all in for $27.78. So the little airplanes, they were $46. So I went ahead and did my whole little pirate ship thing where I did add insurance to those because if that package for some reason gets lost, it's the busy time of year, it's going all the way to California, first class, I wanna be protected. So I paid the extra 80 cents to ensure that first class package over on pirate ship. All in, I was like, I think $5.30 total for shipping and that includes the insurance. So that piece of mind is worth it to me and I showed you earlier in the video how to do pirate ship. It would have cost me a lot more to get that insurance on eBay. All right, I'm shipping out my whatnot orders. Oh my goodness. And I just had an eBay sale and this is a Bolo. It is a blue Santa. I'm gonna pop a screen shot up because I've already got this bad boy package. I tend to breakables since I don't like to ship breakables. I do it when at the time of listing and then it's ready to go. So now I just have to grab it and put the label on it. So this Santa is going out and I can't remember where I got it. Let me look. I didn't make a note, but I think I got it out of a thrift store mystery box but don't quote me on that. So this isn't something I would typically source on my own because it's not really something I'm familiar with and it's also breakable. So I think it came out of a thrift store mystery box. So pretty excited about this big money Bolo. Oh yeah, I forgot to tell you what it sold for. It sold for $93 and the buyer was all in for $108.88. That's with tax and shipping. So I've got 18 different orders going out on, I'm sorry, on whatnot.  I appreciate it very much. These are the bundles. I have a tendency to save the bigger bundles for last. These are people that bought multiple items. I think I sold close to 70 items to 18 people last night. So that's one thing that's really cool about what not is people can bundle. I am doing a mixture of like textures like this is breakable, this is not, this is breakable. So I have to make sure that I'm packaging things so that they are not getting beat up during shipment and damaged. So shipment on these types of items does take a little bit longer. Something to keep in mind if you're going to do whatnot is think about what you're shipping and try to figure out ways to ship it safely so that it arrives safe, okay? That is my whatnot tip. If you're interested in selling on whatnot, I do have a referral link down below. If you use that link, it will say that I referred you and from what I hear I've had a few people already tell me that as soon as they use my link they were accepted right away. So that link is down below. Make sure you click on the one that says to sell on whatnot because there's also a buyer's one. If you use my code to join, you'll get $15 to shop and then you can just use that. You don't have to use it with me. You can use it with anyone. I mean, I'd appreciate it if you use it with me. But again, you can use that with anyone, $15 to shop. If you have not joined whatnot, those links are down below. So if you guys have any questions about whatnot, this is my fifth show. And I know I'm just like, have you guys wanna see my feet? These are my socks. Anyway, if you have questions about whatnot, let me know. It's super, super fun. I should tell you guys a story. Last night, I wish I had it out. You know what? I think I'll save that story for another. Anyway, I didn't know I had. I didn't know what I had because I didn't look and I figured out what I had when I had it. And I'm like, oh my goodness, this is a Bolo. And actually Farm Girl, Scavenger Noelle bought it. So I'm really excited to see what she ends up selling it for. So we'll talk about that in the future. Or maybe I'll let her talk to you about it. So go over and subscribe to Noelle Farm Girl Scavenger. Hey Bolo buddies, this is going out to Cat Feeling Thrifty. She watched my video on my sourcing with Bolo buddies YouTube channel. I had a video. I'm gonna pop it up right here, show you what it looks like. And it was basically items that from my Christmas, whatnot shows, I had four of them. It was items that I didn't get to or items that did not sell. And some of the items only came to one show. And you know, there's only so many people in each show. So a lot of you guys didn't get to see some of those items. So I invited everyone to watch this video and to message me on Instagram or Facebook Messenger with the items you would like and to shoot me an offer. So her items are in this box.  So Cat Feeling Thrifty, thank you so much for your purchase. Thank you also for coming to my what not show. I know you made a few purchases over there also. I really appreciate you. You guys, Cat's link will be, Cat Feeling Thrifty will be linked down in the description if you would like to check out her store. Okay, I think I have some of these listed, but mine do not have the original tag. These are Hallmark Mini Kiss Kiss Puppies. And they actually have a magnet that attaches their mouths and definitely being that it has the original tag is fantastic. Here's a Hippo Webkins by Gans. So typically for plush, what I do is I find comps and I typically will list on the higher end of comps and then I will run a sale and I will add best offer to my item. This one has, it's a little dirty. So when you see my screenshots, I do take best offers that is more than likely not what I'm gonna get for the item. I don't know what this says. Stuffed toy registration number. All right, I sold this little gem. It is a vintage Sterling 1830 O'Merry conceived without sin, metal charm pendant. That's what it says on it apparently. That's what I wrote in the title. And it is, I'm guessing probably Catholic. Sold for $23.55. The buyer was all in for $30.79. This item came out of my bulk buy. I bought it on eBay to sell on eBay. I have tons of videos on that. It was like almost 350 pounds of jewelry that I purchased. So still have an entire tote full plus probably a half a tote that's been sorted and videos have been completed on that jewelry, but I've never listed it. So I may be bringing that stuff to whatnot. Hey, fellow buddies, this next one. What is my favorite thing to sell? Do, do, do, do, do, do, do, do, do. Do, do, do, do, do, do, do. I don't have the tune at all. Do, do, do, do, do, do, do.  My favorite thing to sell is toys. Why? Because they are easy to find. They're usually pretty cheap to source. They are easy to ship. They sell really good. And I'm gonna show you, I'm gonna show you now something I sold. I am so tired. I was up on what not last night until 2 a.m., 2 a.m. I started at nine and I was on there until 2 a.m. selling stuff.  I love it. I love hanging out with all you guys. If you guys aren't following me on what not, go down there. There's a link down in the description. If you've not joined what not, you can click on that link and you'll get 15 free dollars to shop. Even if you come and visit, don't feel like you have to buy anything. Just come hang out and chat. I'd love to see you there and chat with you while I'm live. It's kind of fun. It's actually really fun. And you'll have $15 that you can spend if you want to. And you don't have to spend it at my auction. You can spend it at anyone's auction. So I am Bolo Buddies on what not if you're not following me. Just had a sale. I don't know what I'm gonna do the next one.  And this is my other Bolo Buddies shirt. If you guys haven't seen this one, it's an owl. It says Bolo with Olo.  And it's upside down. How cool is that? Okay, I thought I'd lay these little cuties out for ya. These are Calico critters. And actually these sold for less than I expected. Some of them go for more if you can find the vintage ones that are harder to find. But these were all dressed. And I thought they were gonna do pretty good. They ended up being a little bit long tail. Took a little bit longer to sell than normal. And they only sold for $17.36. The buyer was all in for $25.21. Now I only paid a dollar for them in a garage sale. So that's still a great return on my money. But I have sold some of these in the $50 to $60 range, especially the vintage harder to find ones. So definitely be on the lookout for Calico critters. Not to be confused with Woodsies. I believe Woodsies is maybe the target line. Once you know the difference, like if you search Calico critters on eBay and you search Woodsies, you will see the difference. They look totally different. And it's like, once you know, you know. So do a little research. Woodsies will still sell, but I feel like the Calico critters sell for more. They're kind of flocked. See how they have that like raised material? So they are flocked material. But definitely be on the lookout for these little cuties. And even if they don't have clothes, they still sell. All right, we are headed over to tote 22. And literally when I was listing this, I was like, should I put this on an auction? Because I'm like, what if, you know, condition or year or something like that is gonna cause some variation in the price? I said, common wealth, common wealth. So that one's, I don't know if I'll mess with that one or not because of the tag, we'll see. Oh, look it up. This one has bells. Look at that. Oh, he's so cute. He's big. And it says Darla and Darby. And it's another common wealth from 2000. Here is a Kelly toy bear. My goodness, this is a lot of plush. And this is just one bag. We've got Snoopy peanuts. Oh, his back opens. Wonder what's up with that? We'll have to check that out. Well, let's just check it out. Looks like it has a, some sort of bag in there. That's odd. Huh, I don't know, maybe it's first to put something in. And I went ahead and just put it at a bite now and my sale kicked in. And once my sale kicked in, it sold really fast. So I'm not sure if I undersold this or not. Let's see if I can get it out of here. It's this book right here. And I mean, I looked up comps, maybe I was just like right on target and just happened to be the right person at the right time because you know, that does happen. I sold this for $12.40. The buyer was all in for $16.64. I did, I left this on because I felt like by taking it off, it would do more damage to the item. This is from Kmart and it was originally 64 cents. Yeah, I don't know, did I mess up? Are there any book collectors out there? I mean, it doesn't say like first printing or anything like that or what do you call it, first edition. But who knows, it's in pretty good condition really. I mean, everything looks really good on it. So maybe I undersold it. You guys let me know what you think in the comments. Okay, we are heading over to tote 25. Well, where is tote 25? There it is. This doll came from a garage sale.  Here is another Hallmark cards bear. This one has a button. Cute. This one is Barbie. Oh, it's Barbie. Huh, I don't think I've ever seen that one. I don't know. I'm not seeing anywhere where you open it to change the battery. Oh, wait, there it is, there it is. Okay, so we'll change the battery, see if that works. That one's a little well-loved, but that's okay if it's hard to find, somebody may still want it. This looks like one that you would get from like the fair or something, but it's peek-a-boo toys. And it's broke. So that one we'll probably just donate. Little bear, that one is another Gans webkins. That's a small webkins. I don't think I've seen that size. And we have an emoji poop, rainbow poop. I paid $1.50 for it. And I know she has on a red outfit. So we're gonna see, is this her? Ew, I don't think so. Here she is. It's this little redhead here, I think. I think, I think that's her. Hmm, I think that's her. Let me, let me check. Right here she is. Look at her cute face. She is a Playmates Vintage Honey Doll. And it says 5092 Kellogg's. Says Hong Kong on her neck. And this is the information that was on her heini. So whoever bought these and collected them, I did a video on this a while back. They actually wrote the information on the little tag. So I went ahead and just left that on there. She's not in perfect condition, but she's, her face paint looks really good. Sold her for $13.64. The buyer was all in for $20.99 for her. This is Santa's Workshop Elf Number 25. Hallmark, nice. Let me look that one up. Again, guys, I am simply showing them to you. I will have to research all of these. Precious Moments. This is, I think the Tender Tails Collection. These are usually, yeah, Tender Tails, a bread and butter, but I don't think I've seen that one. There's another little bear. This one is Mall Berry, Russ Berry. And then we have Big Sister. So somebody may be by that just because of the T-shirt. It's by Ebba, E-B-B-A, never heard of that. We've got another little camel, T-Y. I don't usually get the regular Beanie Babies, T-Y. I know some of them can be a bread and butter, but I don't usually mess with them. But if I have multiples, maybe I'll just make a little bundle. Here's a little doggie. This one is by Animal Adventure. All right, so you know the jeans hanging behind me? Well, most of the ones hanging behind me are like flair and bell and they're the bigger, wide leg ones that I have as my curtain. These are a straight crop mid-rise. These are a little bit harder to sell, not as popular right now. These did sell for $20.14. The buyer was all in for $31.65. They are new with the original tag. They retail for $69.90. The black line means that they do this when it goes to a discount store. That way this cannot be returned to the actual store for a credit or for like a credit for something else or actually just a credit to your credit card or however you purchase the item. They also black line the inner label. So what I do in my listing is I put item tag or label has been marked through to prevent store returns. And that is just a disclosure that I put so that they know that what they're getting is gonna have a line through it. Typically, I will take a picture of this tag as well. Okay, so one thing I will say, I really don't sell a whole lot of clothing anymore. This has been a very long tail item, but what I love about clothing is this is a flat rate envelope and I just put those jeans right inside it and they are ready to go. So clothing is super easy to ship. So you spend more time listing it with all the measurements and all of that. But shipping is a breeze. Absolutely love shipping clothing. So a flat rate envelope is a great envelope. For some of you that do not know, there is also a legal size. This is the legal flat rate envelope and you can order these on usps.com also. You can see they are wider. These are great for plus size pants and jeans. They're also great for sweaters and even some coats.  So this is the jeans, which these are great for regular size jeans. Sometimes I can get two plus size items into this one right here. So I usually reinforce it with a piece of tape around the entire thing and then one going this way. And it's not because it doesn't fit. It's still gonna fold at the seam, but more because of when they're being shipped, it can get torn or ripped and it's just more to protect the item. So it just has to fold on the crease and it has to fit to ship. So never had any issues. That is how I do it. And that's just a little clothing tip for clothing resellers that watch me. That used to be all I do. So I have been shipping with these two envelopes for many, many, many years. Great product, free usps.com. I wanted to show you this real quick. We do get a shipping discount when through eBay, but if you're looking at the flat rate envelope versus the legal envelope, it's a difference of 30 cents. So you can fit a lot more in the legal envelope. So definitely recommend those. Those are ones that a lot of people don't know about and don't use and are definitely a great item, especially for just the 30 cents difference in price. All right, here's my booktube. And I just sold this Saturday night live book.  I got this actually free. It was in a thrift store, like outside of the thrift store. Sometimes they just have stuff that didn't sell in the store and they make it free. And it just sits outside for anybody to take. Typically when I do that, I make a donation. So I probably made an extra donation. I usually gave extra money. I haven't been to that store for a while actually, but typically when I would check out, I would give a little extra money anyway because it's a really great cause. But yeah, this is sold on Mercari for $43 free shipping. So I am gonna ship this media mail, but this is a big book.  We got a sock monkey by Kohl's Cares. Kohl's Cares, okay. So for me, I don't typically pick up Kohl's Cares, but I heard the rebel resellers say that she always picks up Kohl's Cares and she gets them listed. I think she said Christmas time they sell. Now she does price them. Usually at $10 or less, if I remember correctly, they are a really major bread and butter, but she says they sell consistently. So maybe that's something I need to be more diligent about picking up. This one is Wish Pets, Montana. Huh, Wish Pets. It's really soft and it's got some beans in it and it's got those big brown eyes. So we'll check that one out. We got Eeyore. He's missing his tail, but that's okay. Somebody might still need him. Okay, we're heading over to the plush. Heading to the plush. Plush tote, 11 right here. This one, I'm going to say is going to be easy to find. That's a good one. I think it is because it's really big. It's a big dinosaur. It's a big dino. Where are you, big dinosaur? Oh, no. Oh my goodness. What? What? Is that it? That's not it. That's a monkey. Oh my goodness. Is this it? Animal fair dino. I think that's it. So I've already got it packaged, semi-packaged. This one I may have to put into an actual box and I'll show you why. All right, so I got it in my favorite box. It's not my favorite box. It's kind of my favorite box. I love the shoe box because everything fits in the shoe box. But right here, this dinosaur is kind of like, well, it's almost a pound and a half. So it has to ship priority mail. Sky sold for $31 all in for $48.90. And I'm gonna show you what he looks like here. So he's really big and he's sort of like that hard plush, not hard, but you know, like more of a stiff plush. So just to protect him a little more, he's got the eyeballs. I'm gonna go ahead and just put him into that shoe box because it's not gonna change the price of the shipment because it's already at a pound and a half and it's under two pounds in the box. So I'm just gonna put it in a shoe box. Lights coming on. All right, I sold some more books. Oh my goodness, they may have the tail and maybe Eore got stained and they need a replacement. Oh, look at this. This is cool. This is from SeaWorld and that looks vintage to me. Made in Taiwan, I don't see. Yep, there is a date, 1980. So that might do pretty good. Vintage little seal there. I think it's a seal. Is that a seal? Maybe it's not a seal. Oh, look at this turtle. I love it. I love turtles. This one is New England Aquarium, 1998. Another vintage one. I love that turtle. That is cool. All right, we're getting to the end here. There is a lot of plush in here. I'm gonna be busy, busy, busy. This is a Angel Bear. It is made by another Wish Pets, Brianna. And not super familiar. I feel like I've heard of Wish Pets, but I don't really know how they comp out. So we will be looking that up. Let's hope they're in this one. Cause if not, I gotta get in the tote underneath this and it is a heavy tote. So these books are from my Ben's Five challenge. I can't remember what that challenge was. Something to do with five. In here they are. I wanna say maybe that one was with Dad Planet. I think these took a little while to sell. But it is these Disney, well, Disney books. And it's a whole set, but it is an incomplete set. So I'll let you know here in a minute what I sold these for. And what the buyer was all in for. These will ship media mail. Okay, so at my Goodwill Ben's, it's 59 cents a pound for media. The buyer paid $23 for these and they are all in for $32.80. So let me just, yeah, one, two, three, four, five, six, seven, eight, nine, 10, 11 books here. Yep, there we go. Walt Disney, they're called Walt Disney Beginner Reader. And I just picked them up because I think I needed a media item for the challenge and this kind of fit that challenge. So there it is. We have this little guy who is a animal junction monkey, shining stars. Not familiar with that, but super cute with its original tag. And it's got, it reminds me of the webkins kind of with the little thing. Okay, I think that's it. All right. There you have it. There's everything. So now I got to get it listed and see what these are worth. Thank you guys so much for being here. Thank you for watching. Just an amazing gift, like I said, and I think I have seven or eight more bags full just like this. So just incredible. And I'm gonna bring these videos to you guys. So that will help all of us learn and we'll keep these educational and thanks for watching.


This is a crazy week we got going on. Swinging in to the crispy to get me a smooth dozen and then I'm heading over to get my buddy Ryan to meet Rob and we're going to a bow archery range. Bow archery. Is that a word? Probably not. Probably just say archery range. Either or. I've been wanting to get my sight tape dialed in and I'll show you guys what that is here in just a second. Right now I've got to get me some Krispies. Don't worry I'm ordering for everybody. That's right. Not exactly the crispiest, the freshest of the creams. There he is. He's getting it. He's getting it. He's an efficient freak. What up man? Thanks for the ride. Krispies. Ooh, how delightful. It's a good morning when Krispies. Krispies. Okay we're here. It's time to do some work. Time to get this sight tape locked in and show you guys what that's all about. I like to let them know what's up. We're at the archery range now. And I got one of the guys here at Sonoma Creek, Dan the Man, to put my calibration tape on. You have calibration tape and then you have your actual tape. This is like 2022-22. You have to choose which number thing it is. Update on these adjustments. So up and down, up and down. I'm trying to get that orange one. It's a dial-in at 20. New dual intro. It's right at the same time. Hey guys. Hey guys. Sorry let me do that again. Hey guys. I wasn't right. Here we go guys. Here's what I might have encountered. A little problem. Look at this thing. Not sure what that's good for. So my sight tape. I've got it readjusted. But I think I might have maxed out my dial. So I don't know. This arrow could go. It could go to the moon. It could go to Hades. I'm not sure. Easy now. A little test pop. A little test pop. We're about to find out though. It's connected. All right. It's going. We're good. We're just adjusting there. Okay. So now it's time. It's time for the racklination. Probably need to go up to that cone right there, buddy. But this might just go into the dirt. Is it going? My arrow by the way. What's that? Didn't lose my arrow. Oh good. Good. Retrieved it? Yep. Good. All suckers are achieved. Am I worried? There we go. I'm not worried. Follow the arrow. See if you got good enough eyesight. Follow this arrow. Follow the arrow. Into the dirt. I'm trying to shoot that deer in the middle of that deal there. Deer. That's a lion. No, no, no. That deer. That's a great target. For a big target. Okay. I don't know exactly. Do you think it's going on the dirt? I think it's going to go right into that board.  Floater. Oh my God. This is going to be low. I can just tell you're looking at the angle. Really? The angle of the angle is going to go on the dirt. Oh. Oh. I don't know. Milked it. No, it did not. Yes. Come on. Hang on a second. Let's take a walk. Is this a lion? I think it milked the turkey. Right? It hit the deer. Also, turkey's feet. Sliced them. But hey, that's what I was aiming for. So elevation could be dialed. How about it, folks? Hey, man. I just got lucky. I don't know. You don't have to shoot anything past 60 this year. I know. I'm definitely not going to do that. That's for you. Sometimes you get lucky. Sometimes you feel like a nut. How many licks does it take? I'm just throwing out random 80s, 90s commercials. What else you guys got? Come on. Hit me with something. Pop it. Spin it. That's good times. Let's get a couple more shots in. Semi-tight. And then we'll be good to go to the next step. Aiming high, aiming low, aiming left, aiming right. Kind of woodland creature are we hitting. Okay, we are low. Oh, we got, okay. There's that one I pulled. Dang. I am a little low still. Crud. I got bad news. What? I got bad news. I got bad news. I got bad news. I got bad news. Crud. I got bad news. What? I got to start over. If I want a consistent bow that I can dial out past 60 yards. Yeah. Or even 260. It's not even exact 60. Yeah, I know. Use it like 50 maybe. Yeah. Because I actually aimed a little high on that kitty cat. And I don't want to have to do that mentally. You're like, ah, better come up a little bit. Starting over. Dialed out. I was all the way maxed. Yes, I'm close. You know, there's a, I hit this cat here at 60 yards. Pretty good shot. But what I had to do was mentally come up to about right here on the cat. Because I knew after shooting a consistent grouping about right there. Five or six inches low. I have to make an adjustment up and I can't come up anymore. That means I got to start over. What are you doing today? That's here's the thing with bow. You get tired. Yeah. You're not going to shoot the same. So I'm going to get them to adjust it. And then I don't know. Oh, that just pulls this whole cavity out. If you're going to do something though, better do it right. Such a process. So hopefully we're going to be able to come out here. Pop this kitty cat right in the heart and lungs. And then we'll know. Actually, I'm probably not going to use the kitty cat. I'm going to use an actual target. And then I got to go back and make fine tuning adjustments to the pins themselves to make sure the 20 and the 30 are on par. And then what we have is a cool system where I can take that 40 pin. It's called the floater pin and dial it out to whatever I want to dial out to 100 yards. It's not realistic situation. And we all know that my hunting season this year is probably going to be cut short due to a little Emmy. Had to get things dialed in on a short basis last year as well with brain surgery. So anyway, I've been wanting to do this for a while. We're taking the time to do it today.  Made our adjustment. Put our spot hog at the 20. Almost shot a bull. I'm shooting at the deer, but I almost shot it in the heart and lungs and it's a tiny little deer. It's only about a foot tall deer. As long as you can shoot a pie plate at 60 yards on a consistent group, I hear that's decent. That's okay. So that's what we're going to see what we can do right now. If I'm in the deer, I'm not touching it. I'm in the deer. Off three of them. We are pie plate central here. That's what I was getting mine into before I went inside. Oh yeah. You were probably actually just working on aim at that point. That's good. That's dead dares. That's a little tiny deer. He's like, what, foot and a half tall? He's dead. Rob spent probably four hours out here dialing in at 60 yards to where he was hitting a squirrel's head. And then he goes in there and they're like, well, you really, as long as you're hitting within a pie plate, you're probably pretty dialed. He's like, good. I just spent two hours of my life trying to hit a squirrel. As long as there's consistency, at least for me, I'm not trying to hit the archery tour anytime soon.  The main mission has been accomplished, y'all. I still need to do the fine tuning of the pins themselves. I can actually do that at the treehouse. But what happens when you're shooting that many arrows is your shoulders, your little muscles start getting tired and then you start getting a little wobbly. So I noticed when I went back in to shoot at 20, I was left, right, high. And then I just said, you know what, it's time to shut it down. Hey, I got to work on my brain, y'all. It's time to go down and visit the doctor. I got to get up early in the morning and go see what's happening inside of my skull. Okay, after a extended period of break time, I'm ready to go again and finish this thing off.  I apologize for the cicadas. Gosh, dang. That's how you still know it's summer right there. Cicadas. Any guys know the life history of cicadas, by the way? It's super weird. Google it. We haven't got to enjoy the outdoor aspect of this house very much yet because it's just been so hot. I mean, Steph's pregnant. She hardly even goes outside in this Texas heat right now. But this is an incredible outdoor space. I mean, we're close to the lake. You know, I got the bass boat over there. We have these woods. We have nature and everything. But the way these trees are spaced out and the elevation capabilities that I have with the tube decks makes it the ultimate place to practice archery for deer hunting out of a bow stand. I'm going to memorize these trees with different garages so I can go 20, 30, 40, 35, 25, whatever. So every day I'm home, I can come shoot. I can start memorizing distances. That's another thing is just having those trees and having that scenario where you're elevated, looking, and then just using your rangefinder to just get a feel for the distances. You know, you only have a few seconds usually when a good buck walks out to make that shot. So if you already know, gosh dang it, cicadas. Oh, I know why. Whoops, forgot to dial it back. Yeah, we're doing it now. So that's my last shot. That's when I had it on 40. My 40 pen right here, I've messed around and I had it dialed to like 35. So both these shots are straight in line. The elevation was just wrong, so I adjusted it back to 40 and thumped it. It's time to test this site tape out, guys. I'll show you why I went through all this trouble. Okay, this is where it gets really fun right here. You guys see this target over here? I don't know exactly what distances it is. Because I just flung it out there. I'm not getting a good read either. 33 is what it looks like. I'd like to get a little bit more distance than that. Let's scoot back. Let's see what this is right here. 34, okay. 34, right at 34, it's about a 35 yard shot. Now normally I would have to go in between my pins in this situation, but let me show you what this thing does. So this is the site right here. And what this allows me to do is dial out to a specific area, a distance. So I have my pen. I have my orange pen right here. If you guys take a look at that orange pen, that is my bottom pen. It's my floater pen. Now it's set at 40. So if I shot at 40, that should be on. Green is 20. Red is 30. But when we come over here, that's on 40 right now. So if I'm at 34 yards, so if I know that with my rangefinder, all I have to do is adjust this and I'm going to go, there's 35. And we'll just eek it right in there at 34. Oh, yeah. So these are my first two shots right here, which got in the white. That one's touching, but that one's in there. This last one I pulled, I pulled high. That's pretty awesome. So I can dial this thing out. I'm not a good shot at long distances. I don't practice that much, but I definitely will. Let's just say you get in a situation where you're in a stand and then there's a buck that's walking in the field and then he's not coming in the tree line and then I don't have a pen for, I don't have a pen for 60. Dial this thing out and then bam, you can get exactly, you can at least take a shot. If you feel good about it, you can take a shot. There's a rabbit right there. Little bunny. I'm pretty surprised to see a bunny right there and he's being really calm around me, but I'm surprised because there is literally a fox den. I've recently found a fox den probably 40 yards behind that rabbit. And so anyway, they usually clean up the rabbits and the squirrels and all the ground animals.  You better watch out for the foxes because they're right over there. I got a little Amy on the way. I've only got a couple of hunts. You got to make them count. All right, make every hunt count. That should be a thing. Make every sit count. It kind of works. Anyway, that's my philosophy. Thanks for tuning in today, guys. I'm not a bow expert, so if you're looking for bow expertise, I'm not the channel, but I do like to show you guys things that I am trying to do or I love to do and then walk you through them. And I try to do a good job showing the steps, but if I miss something, let me know in the comments down below. This is one of my last videos in town this week and then I'm heading to Houston to go see the brain surgeon and then I'm actually heading up north for a few days. So go ahead and sub it and follow me on the socials, guys, and I hope wherever you are, you're having a blessed day. And I thank you guys for being here. I love you and I'll see you on the next one.


What if all we had was one particular book of the Bible? Would that be enough? Especially if it's one of the New Testament books, Matthew, Mark, Luke, John, 1 Corinthians, 2 Corinthians, Acts, you name it. Would that be enough? Because what we forget sometimes is that the way we see the Bible is not necessarily the way that those at the time of the writing of the Bible or even immediately after the Bible was completed, how they saw it. Because remember, they didn't have access to all of the books. They may have heard of the things that are entailed in some of the books, but let's say all you had was the book of Romans. That's the only letter that you had. Would that have been enough? Well, sure. Certain books, without question, we would know enough from that book. What if all you had was the book of Matthew? Same thing.  What about the book of John? And I think that book, even more so than the other books, would give you far more or at least enough to live off of, to understand what the gospel is, to understand how you ought to live, to understand what God is doing. And so if you had just the book of John, which you're going to look at, would you know enough? Because I think there is this misnomer that states that a proof text is a bad thing. Well, it's not. Because remember, every word that's given, especially if you could understand the context of that particular proof text, well, then it's not a bad thing. Now, should a proof text ever contradict any other text? No. If it does, then we've got a bad understanding of that particular text or at least the context of that text. But when you look at the book of John, there is a lot of hemming and hawing over certain things that are stated. And I just want to go look at it, particularly in John 6, starting in verse 37, working our way down to verse 47. We may go a little further, but I want to see is there a way to look at this particular book, this particular chapter, the set of verses in this chapter? Is there a way to look at it differently? For example, you all know that I believe that a person cannot lose their salvation. So when I look at these passages, if I believe the opposite, if I believe that you could lose your salvation, how could I take those passages to believe that? Is there a way or do I have to look at these passages, kind of shake my head, go, hmm? and then say, okay, but these other passages, because what if all I had was these passages? What if all I had was this book? So it couldn't be that I need the other books to understand John, particularly John 6. So I want to look at this and see, is there a way to look at these passages to see if maybe the other side could be, you know, there's some validity to what they're saying. So if I go to John 6, let's say where do I, I said I'll start from verse, let's start in verse 35. Jesus said to them, I am the bread of life, whoever comes to me shall not hunger. And by the way, we're going to have to, because we want to do an in-depth look at this, we want to look at it from the Greek. The person that comes to me, Ha-ekh-e-menos, the person that is coming to him, umay panase, which is will never hunger. And this is the emphatic double negation. This is a double negation of a subjunctive. So when we see a double negation of a subjunctive, it is one of the most emphatic ways of saying it can never, ever happen. And because it's a subjunctive, the possibility of it happening can never happen, even in the future. That's what's implied, that's just the rule. Okay. So if I say they may never hunger, I mean with the umay, they may never, ever, ever hunger, no matter what happens in, even including something in the future. So he says the one coming to me will never, ever, ever hunger. And the one believing, this word is important also, ha-pistuan, remember, every time that the Bible describes a believer, not every time, but most often it's someone who is in this, with this participle, this is a present active participle, this person is believing. So the one, the believing ones that's in him will never, ever, ever, same thing. Thirst, dipsesae, which is also, now this is not a subjunctive, unlike the word for hunger is a subjunctive, this is a future active indicative. And so the two most emphatic ways to deny something from happening are here. This person will never, ever, as a matter of fact, the never ever is also added to it just to give even extra emphasis, but this person can never, ever in the future thirst. Meaning they came to him, they believe in him, and so whatever happens, whatever's going to happen in the future, it seems to be signifying that they will never, ever thirst. Well, that's kind of going to keep them with what we see in John 4, right, when he's speaking to the woman at the well. So it'd be hard just so far grammatically to say, well, I can see a person not being saved, a person losing their salvation according to this, because you have to keep believing. You have to keep coming, but is that what the passage says? It says the person, now it does use the word whoever in English, but the word that's used here is a commandeuce, which is the person that's coming. This is the person, this is the middle participle, it's with the middle voice, as a participle. So this does kind of convey coming often, all the time, the ING part, so fine, but then the person's believing. So is this saying that if you keep coming, or is this saying that the person that is coming, that's what they're doing, they're constantly coming, same thing with the person that's believing. I don't see the condition there, and there are some words in Greek that we can look forward to say, well, I see the condition, an if, and there are different ways to say that in Greek. You can say that eon or an may, if or if not, unless there's a hati, there is henna, those words kind of indicate that there is some sort of condition or the reason why something has happened. And then we get to verse 37. We haven't gotten to verse 37 yet, verse 36, but I said to you that you have seen me and yet do not believe. You see me and yet you don't believe. Verse 37, all the Father gives me will come. Now, the question here is, is there any way to where we can make this verse dependent upon us? Is there any way to make this verse have some sort of condition? Meaning if we keep coming to him, then we'll be the ones that the Father will give. And then by that logic will also come. You can't say that there. You can't, you can't apply a condition, at least I can't see one. You can't apply a condition here in verse 37 because the condition or what's happening has nothing to do with you, even though it affects you. It says all that the Father gives pan-ha-de-dosin, all the Father gives, and this is the present act of indicative. It doesn't necessarily mean that he's going to keep giving, but I would say that all of the Father is giving. Not always will it mean that, but I think in this case it does mean all of the ones that he is giving to me, the Father, to me, they will come. So he says that all the ones that he is, and I'm trying to stress this importantly, there's a reason why, all the ones that he's giving to me, all the ones that the Father is giving to me, they will come. And this word here is hexae, which is a future active indicative, Jesus is stating that they will come. Who is the they that will come? All the ones that the Father is giving. So whoever that is, Mary, Frank, John, Marty, Gino, Herschel, Betty, whoever, whoever's included in the all, he says they will. And so two things can be stated from this. All of those people were given to Jesus by the Father, and all those people will come to him. I think that part is pretty clear. It'd be hard, difficult to see any other way. And the ones coming to me, I will never, ever cast out. Now this word air come in, let's drop back, go back up, because it's not the first time we saw this, even in this chapter, it's the same word that's used here. Those who are coming to him, so the ones that are coming to him are the same as those that he gave.  The ones in chapter 635, he says the ones that are coming to me, so we couldn't even add a condition on these people. The ones who are coming to him shall never thirst or hunger. He's also stating that the ones that are coming to him are the very same ones that will come are the very same ones that he gave. Okay, I think that's important, because thus far, I just don't see thus far how a person can say that there's a condition attached to us that we have to keep doing this. So the ones that are coming to him, which are the very same ones that he says will come, which are the very same ones that were given, he will never, ever, ever cast out this Ume Egbalo. This is also the heiress active subjunctive, so he will never, ever, the possibility of him casting them out is gone, no matter what happens in the future, because that's the rule. Then he says, For I have come down to do the will of my Father. So he even tells why he gives kind of a reason, a little added reason as to why they won't be cast out ever. This word, hati, this is a condition that's added to it, or the explanation as to why, because he has come down from heaven not to do his own will, but the will of him sent me. So the reason why they won't ever be cast out is because of this will of the Father that he's come to do, and this is the will of him who sent me, that I should lose none. Here it is in order that all of the ones, and I want to focus on this word right here, let me highlight this, this word henna, this all or this henna, it is what's called a purpose, it starts a purpose class off. It's so that this is the reason why, the purpose of this, the purpose of him coming is so that all of the ones that were given to him. Now, this part I want to pause a little bit, I want to really get you guys to see what's happening here, because I think just so far, I think it just solidifies the impossibility of a person who has been given to Christ to ever fall away, to ever leave. Let's go back to it. The reason why he came, the purpose of him coming, this henna, in order that all of who, all the ones, now notice this is in the perfect tense. The perfect tense is a completed action from the past. So all of the ones that had been given to Jesus by the Father in the past are the very same ones that as far as we know, he's still giving. What does that mean? Mary, John and Frank, who are not saved yet, who will be saved, they are the ones who are, who God is giving. But Jesus makes the point known, because this word here, the doken, perfect tense, he had given them to Jesus in the past. So he gave them to Jesus in the past, though he's giving them now, we see them as being giving now, being given now, but God gave them past tense, perfect tense in the past. And all of those ones that he gave in the past to him, to Jesus, he says, may apaleso, which is they will not, he will not lose any. He will not lose any out of it, out of what? Out of the it, the out to is out of the ones that were given. He will not lose one out of the ones that were given, but he will raise them up in the last day. So far it again to me, and I could be wrong, I don't see it though, I'm trying to use English and the Greek, the Greek even more, so we see this a little bit more clear in the Greek. There's just no way that a person could find their way out of, because so far, thus far from verses 35 through verses 39, we don't see the condition upon the man. We don't see that this person has to do something to be in him and to stay in him. We just don't see that. Well, Corey, are you saying that a person doesn't have to believe? Of course a person has to believe, but implicit in what's being stated here is that the person will believe because they were the ones that gave him. How do we know a person will believe? Because he says, Jesus says going back up to it, he says all that the ones that he's given, he says that they will come. All the verse 37, I'm sorry, all the ones that he's given, he says they will come to him. So the coming to him means they will believe in him. How do we know so? Because in 35 he says these are the ones, the same ones that are coming to him, and the same ones that are believing. So what has to happen in order for you to be saved, the coming and believing, he says they will do. Are you guys with me so far? So now if we drop down to verse 40, let's pick it back up for this is the will of my Father, that everyone who looks on the Son of the Man, and by the way, the word that's used here is the Eorom, which is a part of what these people are. Notice again, the Bible describes us as in this state of doing so. There's this, the aspect that's given that we are going to be continually, in this case, looking on the Son. We're going to keep believing on the Son. This is the will of him, that those that the ones that are in order that all the ones that are looking on the Son and are believing as a word, Pistawan, that are believing in him, they have life. Notice this statement right here. They have ecate, it is present tense. They have it.  Same statement. So so far, Jesus has been pretty clear, as clear as he possibly can be now. Is there another way that I can think of? I can't now, Greta, I'm not some great Greek scholar, but thus far, I can't think of a clear way that he could have put it to state that I'm going to give these people to my Son and all the ones that come to him, the Son will never ever cast out. He, as a matter of fact, he won't lose any. So whatever way that you want to try to couch this, that the person could leave on their own, walk away, stop believing, Jesus says that he will not lose anyone, not anyone. Okay. I don't, I don't know if there's a clear way that he could have put it. If there is, I would love for someone to say so. Someone to say, well, Corey, if he, he didn't mean that. So my question would be, if he didn't mean that he could lose not one and none would ever perish. What is the Greek way to say? What's the Greek way to say that they will never ever perish, no matter what? What is the Greek way to say that he, it's impossible to lose someone? What's the Greek way to say that if you are saved today, you'll never be unsafe? What is the best Greek way to say so? I would love to hear that. The question is, or the problem is, there is no great Greek way to say it other than the way that he said it thus far. That's the problem. Let's go back to it. Verse 41. So the Jews, the Jews grumbled about him because he said, I am the bread of life. I'm sorry, the brother came down from heaven. They said, is this not Jesus, the son of Joseph, whose father and mother we know? How does he say, I have come down from heaven? Well, they're missing the boat, aren't they? Jesus said to them, do not grumble amongst yourselves. No one here, he's shooting at them right now. He says, no one can come to me unless, and here's the if or the unless that we said earlier that's missing as a condition for being saved. Earlier, Eon made, unless if not, that's what that's these words right here. Eon is if made, not so if not or unless the father, the one that sent me, if he draws them, unless he draws them, he says that that's the only way, unless if not, the father draws you, you cannot come. And I will raise him, and Jesus, what does he do? He reiterates what he says, and I will raise him in the last day. He's already said that twice is the third time he said, I will raise him in the last day. Raise who? The same one that the father has, that the father draws, the same one that the father gives or has been given, that it is giving and has given. The very same one, the very same one that he says he will not lose, not won. The will of him is to come, in order that he would not lose one. That's important, by the way. The will of him, he came to do this will. In order for him, in order for no one to be lost, he came. Why is that important? Well, remember, backing up a little bit, Jesus makes this statement also in John 3, and he's piggybacking off of everything that was stated in the Old Testament. Under the Old Covenant, your sins can be atoned for, but you could still thereafter be lost. And so he comes, in order that none of those would be lost. Let's go back to verse 44. He says, And I will raise him on the last day, again, reiterating what he's been trying to get across through our, or their thick heads. He says, Is it written in the prophets? And they will all be taught by God. That's a, guys, that's important. That it has been written in the prophets, and they will all, all. Who's the they? Not just everybody. Obviously, but he's speaking about a certain all, those that have been given. All of them will be taught by God. Very important. And so everyone or all the ones that hear, or heard, and I'm sorry, the father from the father, and learn from the father, that person comes to me. So if you've heard from the father, notice how he puts that, though, as well. I think that's interesting. If you had heard from the father, or heard from the father, put it the way, actually the way it's written, heard from the father, and have learned from the father, what does he say? You, you will come to him. He's even using this, the basic past tense. If you heard, this is Eris active participle, have heard or have been hearing, then you will come. Not that anyone has seen the father, except he was from God, he has seen the father. Look what he says.  Truly, truly I say to you that whoever, and the word whoever is not really the word whoever, it's the hapista one, the one that's believing. And we've already discovered and discussed and determined who the one that is believing is, that very same person. He has, so if you believe, the person that believes, he, aka Zoe Nounian, he has life at that moment, at that very moment, right now. That's the whole point of using the present active indicative. Right now, that person has. Remember, words have meaning. Even if we don't understand the words ourselves, that doesn't negate the fact that they have a meaning. Because we're ignorant of it, doesn't mean that we should make everyone else be ignorant of it. Because we don't know, doesn't mean that no one else could know. And so when someone is showing you, we're showing you now that if you believe you have it right now, life into the ages, you have what now? Life. How long do you have it? Into the ages. So where does that stop? It can't. So he says, your fathers ate the man in the wilderness and they died. This is the bread that comes down from heaven so that they, so that the one, so that one may eat of it and not die. So that one may eat of it and that person would not die. I am the living bread that came down from heaven. If anyone eats of this bread, if anyone eats of this bread, he will live forever. And the bread that I will give to him for life, for the life of the world is my flesh, meaning what? I'm going to die for them. Why is that important? Because what Jesus is stating that when I die, I'm going to fulfill what the law required. I'm going to atone for sin. My flesh is what I'm speaking of. I'm going to give it as a ransom. So that way, that's what he meant by in order that all the bleeding ones will never perish. So as I look at this passage, as I look at this passage, I don't see one, if you notice, there was no condition in this for those that are his. The only condition that's put about is that the only way that you can come to him, the only condition that we see thus far is that he has to do it. He has to draw, which makes sense because he says that all the Father gives. So if the Father didn't give, meaning that he didn't draw you, then you can't say that you will come. He says those that he did give, those that he did draw, they will come and he will not throw or cast out any one of them. I just can't find a way and I've tried to. I promise you guys, I've tried over and over and so I have someone. If there is, since words have different ranges and nuances and so forth, tell me those that would disagree or even those that agree, ask your friends, who would disagree? What would the Bible have to say for you to believe that you can't lose your salvation? How would the Bible, how would Jesus have to put it in order for you to agree that you cannot lose your salvation?  More than likely, he said it. I'm pretty sure he has, but I would love to hear what someone who disagrees, what is the emphatic way to say that you can lose your salvation? What is it or what is the emphatic way? I'm sorry, what's the emphatic way for Jesus to say, or the Bible say that you cannot lose it? What is that way? How would you say so in Greek? But until then, we see how Jesus says, these are His words. These are not my words, these are Jesus' words. And so the question is, if you're not going to take these words, and instead, you're going to go to other passages and look and look and look and search and search and search with all your fervor, with all your heart to find a way for this not to be true. Now we've got a problem. So I would be interested to hear what someone has to say. I would love to hear, I would love a response. And I'm going to get some, but they won't, but when we give the response back, I say, okay, this is how you could say in the Greek, how you can never lose your salvation. And then we say, okay, well, he just did. What will be the response? Likely they'll deny that as well. So for those of you, though that are looking for more encouragement, and I think it's important that you be encouraged to know that this is the confidence that Paul has in us, about he who began to get working us. The same confidence we can have because Paul, Paul, the writer of Hebrews says, you will have need of this confidence in this day. As more and more things are happening, you will have need of this confidence. You need to be confident that what God has done, he has done completely. He's going to finish it.  You don't have to be in despair. You don't have to be in doubt because what God has done, he's promised to do and he will complete it. Amen.