Let's take a look at a few more root equations. So our ability to solve root equations is based on the idea that if the nth root of x is equal to a number, then a to the power n is equal to x. So if I have square root of x plus 5 equals x minus 1, I can start by squaring both sides. And let's clean this up a little bit algebraically, expanding. And because we get a quadratic equation, let's get all of our terms on one side. So after all the dust settles, our original equation has been transformed into a quadratic equation. Now we can solve this quadratic equation any way we like. And today we like the quadratic formula. So let's use that to find our solutions, which are going to be 4 or negative 1. Remember, we always need to check to see if these are actually solutions. So we'll check x equals 4. We'll substitute that into our original equation. And since the square root of 9 is actually equal to 3, this is true. So x equals 4 is a solution. We'll also check x equals negative 1. It's important to remember that principal square root of A always indicates a non-negative number. And so this statement, principal square root of 4 equals negative 2 is false. So x equals negative 1 is not a solution. And we should indicate this when we write up our answer. All right, let's take another example. Now remember, we know what to do in the case of root equals, so we need to isolate the root. So right now we have square root plus 1. Let's get rid of that plus 1. And if we subtract 1 from both sides, we now get square root equals. We can square both sides and simplify. And because this is a quadratic equation, let's get everything on one side. And that produces a corresponding equation. Solve the equation any way you like, which gives us solutions x equals 5 and x equals 1. And now let's check our two solutions. Checking x equals 5 by substituting it into the original equation. And we get a true statement, so x equals 5 is a solution. We'll also want to check x equals 1 by substituting it into the original equation. And this is also true, so x equals 1 is also a solution. So both our solutions are solutions to the original equation. Or we could take a look at another example. This is already in the form square root equals, so we'll square both sides. And we'll solve this somehow. And remember, if you don't write it down, it doesn't exist. So let's summarize what we've done so far. And of course we'll circle our answer. And because we did this, our answer is completely wrong. Because any time we're dealing with a root equation, we always have to check to make sure our solutions satisfy the original equation. So let's rewind. Checking our solution, x equals 2, does not make the original equation a true statement. So x equals 2 is extraneous. We'll check x equals 1. And again, x equals 1 also makes a false statement. So x equals 1 is also extraneous. But these were the only two solutions that we had. And since both are extraneous, this equation has no solution.  And a useful idea to keep in mind is that anything you can do once, you can do multiple times. So in other problems, we isolated the square root and got rid of it by squaring both sides. Well, let's try it. So the left-hand side has two square roots. So let's get rid of one of them. So maybe we'll subtract this square root 4x minus 3, and we do have to do the same thing to both sides. So now I have square root equals mess. Well, I can square both sides, expanding the right-hand side, and we can do a little bit of algebraic cleanup. And remember, if it's not written down, it didn't happen. But wait, we still have a square root in this equation. Well, let's isolate the remaining root and square. So we'll rewrite the equation so the square root term is on the left, square both sides, and do a little bit more cleanup. And again, if it's not written down, it didn't happen. Now we have a quadratic equation, so solve this by using your favorite method. Now maybe your favorite method is having the solutions fall out of the sky and hit you on the head, but a slightly less hazardous approach can use things like completing the square or the quadratic formula. And again, the important thing to do with any sort of root equation is to always check to make sure your solution satisfied the original equation. And when we do that, we find that x equals 1 is a solution, but x equals 13 is an extraneous solution.


you need to take care of email ID of dependents. So if you're booking a visa appointment with your dependents, then each dependent also has a profile and that profile needs a email ID. So it's recommended that you give individual email IDs. Right now you might have given your email ID or maybe a common email ID, but make sure that individual email IDs are updated for each of the person applying for a USA visa appointment.


Welcome to my talk. Hopefully, you love it by the end of the rambling that I do today. How many of you guys use Sketch right now? This is interesting. OK, how many still use Photoshop? Oh, I don't know. We got to change that today. So let's go to the second slide. I want to start off with who am I? So my name's Nora. She already kind of introduced me. But I wanted to give you a little bit of background. So nine weeks, well, in 2015, I went to a coding bootcamp called WinCode. How many of you guys know about it? Awesome. Well, I went there. I studied Ruby on Rails. And at the end, I'm like, OK, I love this. But I really love design. How can I merge both worlds into one? My first job was at Sautoglobal Solutions. And that was the place I was able to do all of that. I was able to mix my UX design kind of background. Also, my front-end development knowledge that I learned from WinCode while I was there. And honestly, it was a lot, trying to combine both of that knowledge. My words with companies like Magic Leap while I was there, Under Armour, BCBG, Kate Spade, so many different retail clients. And I'm like, OK, how do I come to you guys today to explain why using design and development skills are very important? So let's go to it. So this is a list of all design tools. I am not saying learn all of them. Do not learn all of these. But I feel like there's a few here that can really expedite your development skills and your development time frame that you have. These are the two that I'm really, I want to nail down and talk about. So Sketch and Zeppelin, how many heard of Zeppelin? OK, that's good. So here, I'm sure you're asking, why isn't Photoshop on the list? So I'm not going to bash Photoshop right now. Photoshop is awesome. But Photoshop is mainly for photo manipulation. It was not designed for user interfaces. It was designed specifically for photo manipulation. Now, you can still use it, not saying, you know, throw it away or anything. But I believe that Sketch is better for user interfaces. So let's go and compare. Photoshop versus Sketch. So in my opinion and in a lot of other people's opinions, Photoshop is very bloated. It's complicated. It's for photo manipulation. While Sketch is simply simple, you can use it for user interaction or interfaces. And you can also use a lot of the libraries that's already come with it. It comes with so many different things already loaded on. And it basically streamlines your entire process. Second one, say goodbye to your RAM if you're using Photoshop. It's going to slow down your computer. No, it's not ideal at all. While Sketch is very lightweight, perfect for developers, perfect for the environment that you have, because you're going to have a lot of different development environments already running. And it's best to use Sketch for that price. So Sketch, well, Photoshop starts at $19.99 and it ranges from $79.98 per month.  While Sketch is a one-time payment of $99. Now, put the asterisk there, because with Sketch, you have to upgrade every year to make sure that you're able to get all of your software updates every year. But if you do not do that, it's OK. You can still use your same $99 Sketch license. Sketch is also with Mac only. Photoshop is Windows and Mac. But there is a way that you can also use it on Windows if you use a virtual machine. So here's the differences. Let me see if I can play this. All right, so with Photoshop, you're able to use smart objects. I'm going to try to speed up. But smart objects is awesome, but you can't create dynamic layouts. With Sketch, you're able to create dynamic layouts. You can use your overrides right here on the side there. You can automatically change things right then and there. You can change the contents, everything here. And it's very seamless. You can change your active states for your navigation bars right then and there. You create one button. And that serves the purpose of all of your buttons that you'll ever use in your Sketch file. Here's some plugins that can speed up your development. So I know I already talked about Zeppelin. So Zeppelin allows you, how many of you guys remember redlining with Photoshop? It's probably old, but yeah. I used to use it back when at my first job. But with Zeppelin, you're able to upload these and get all your padding, your margins, your fonts, your sizes, your colors, everything right here, no matter if you're on Windows or on Mac. You're able to also get code snippets. So you can focus on functionality only. You don't have to dig deep into understanding which CSS applies to what. You can just focus on the functionality and also when it comes to exporting, it exports in all of your sizing. So you don't have to worry about having all those folders upon folders of assets. It's right then and there. Prototyping. So from here, with Sketch plugins, you're able to prototype. So here's all different prototyping tools. I usually use Envision. So you're able to link all of your screens, show your clients exactly what they're going to be using or looking at before you code it. That can save so much time. You guys don't understand. When I was a freelancer, I still am. Usually, this part was probably the most aggravating part. Trying to code something, they say, oh, no, I don't like that. You have to recode it again, prototype it so much easier.  So Sketch has allowed us all to prototype right here in the Sketch application. They've upgraded not too long ago, maybe a few weeks ago, and you're able to prototype right then and there. You'll see in a few seconds, let me wait for it, you're able to view it on any application. So if that's web, on the phone, you can show everybody in your team how all the prototype or how your design is supposed to work without you having to code it. So let's wrap up. All right, so Photoshop is better for photomaniap... Can't talk, manipulation. While Sketch is for user interfaces, Photoshop is pretty heavy on your machine while Sketch is lightweight. Sketch is awesome when it comes to libraries. Sketch Library allows you to work and collaborate amongst your entire team. You can share your styles and your symbols across all art boards, across the files, across everywhere. You don't have to recreate the wheel here. On Sketch plugin, Zeppelin allows you to export on the fly, copy the CSS code snippets, and implement designs pixel-perfect. And the last thing is before you jump to code, prototyping is your best friend. Please prototype before you have to spend too much time. So yeah, that's it. Here's the information on me.


Welcome back. We're set for first conversation this morning and of course that we'll advertise rising from an emergency session and its first meeting of the year. The National Economic Council has endorsed the Nigeria Agenda 2050. It's designed to take the country to upper middle income status and subsequently to the status of high income country. At the meeting presented over by the head of the chairman of the National Economic Council, Vice President Yemio Shebajo. The Agenda 2050 was presented by the Ministry of Finance, Budget and National Planning to the state governors and other members of the NEC, including federal ministers. Speaking after the presentation and discussion by council members, the Vice President of Nigeria, Professor Yemio Shebajo, in a statement by his spokesman, Laolu Okonde, observed that the plan, quote, captures a lot of the expectations for Nigeria in the future and hopefully implementation which is key if effectively done. Also commenting on the agenda of the Agenda 2050, Minister of State for Budget and National Planning, Prince Klem Agba said the federal government is keen or has taken steps rather, which are unprecedented in ensuring the operationalization of the plan, especially with the inauguration of the Staring Committee of the National Economic Council. Are we asking what does this creation of a development plan mean for Nigeria? We're glad to have Nika Gulli, a public affairs analyst, join us to discuss this development. Nika, good morning to you. Nice to see you. I can see Nika not smiling. I can see a slight smile. I mean, you should be really beaming smiling from ear to ear with the President's announcement this morning. There you go. Thank you so much, Kofi. Good morning. Merci. Good morning. Good morning, our viewers all around the world. Yes, I'm not smiling because this is a country of confusion. The Supreme Court has made a ruling and once that happens, rule of law demands that everybody, including the President, should respect that. And if the President is not happy with the ruling of the Supreme Court, President needs to go back to the Supreme Court and get the Supreme Court to upturn himself. That is the independence of the judiciary. We have three arms of government and the President cannot be carried on as if he is a law upon himself. So that is why I'm not happy about what the President said this morning. Okay. That being said, let's look at this development plan that the Vice President is talking about. And of course, through the National Economic Council, as we earlier said, and for those who are wondering, what exactly do development plans do for nations around the world? Of course, you know how the Chinese do. They have the most popular, the most famous development plans in the world. We're looking at, like they said, taking Nigeria to upper middle-income status and subsequently high-income status. We're looking at gender 2050. What is the role of development planning in the development of countries like Nigeria? There is a maxim that says if you don't plan, then you plan to fail. Everybody needs to plan as individuals, as corporate entities, as families. Just everybody. You have to have a plan. So a development plan is a strategic long-term plan by a nation to chart the way forward. To say in X number of years, this is where we want to be. And that is planning for everybody. A family must also have a plan whereby you say, this family, where are we going? You can't just be going about endlessly. I mean, you cannot start a journey without knowing where your destination is. So a plan is basically to set the structures in place for your destination. That is, for Nigeria, with a gender 2050, we are heading to this direction and by 2050, we want to arrive at that destination. So in a nutshell, that's what the plan is. It's a future statement of where you want to be. But the plan has to come with concrete steps as to how you are going to arrive at that destination. So I'm in Abuja now. If I want to start a journey and I say that I want to be in Makodi next week Tuesday, I have to have a plan on how I'm going to. Okay, we seem to have a network interruption with Nick Agule there. Nick, are you back? Okay. But interesting, of course, Nick has rightly given us the importance of this national plan, development plan, you would call it. Nick Agule, if you're back and can hear me, please continue with the point you were making. Yes, yes, I'm back. Can you hear me now? Loud and clear, we can. Okay, fine. So I was saying that a plan is not made for the sake of, say, you make a plan. You make a plan and then pack up that plan with concrete steps on how you are going to get to that intended destination. So I was trying to give the analogy that I am in Abuja now. I have the intention of going to Benway to vote next week. I can't sit here in Abuja and say I'll be in Benway next week to vote when I have not put what will take me to Benway. Am I going to walk? Am I going to cycle? Am I going on a bike? Am I going to go by a car? If it is by car, am I driving? Am I going to go by commercial vehicles or how? So if that is not the how, then the plan just remains a plan for the sake of planning. Next week we come and I'll be in Abuja because I didn't put the how in place. And that is what is lacking in most of Nigeria's plans. Well, I mean, I like the fact that you said that that's what lacking in most of Nigerian's plans. We've had several development plans as a nation and you want to ask yourself, should we be excited about this plan? Making reference to the previous plan. One of such is Vision 2020. Now Vision 2020, if you ask yourself today, where is Vision 2020, what happened? Now, from the onset, there were several criticism behind the major targets of the vision. I wanted to juxtapose that Vision 2020 with Vision 2025 and answer if you think that this vision is going to see the light of day or if it's already set out to fill. Now, the Vision 2020 was set out to propel Nigerian to the league of 20 best economies translating to having a GDP of at least $900 billion by 2020 when you compare that to what we actually made in 2008. And so I ask you, do you think that these 2050 vision agenda that we have is very realistic? And you know, it meets the needs of the people that it's there's a connection between the people and this plan or this policy. Thank you very much for that question. First, I am not excited at all about this plan. Totally not excited. Coming off the backdrop of what you have just listed now. We have had plans in the past that have just remained plans on paper. You know, we had oppression of feeding nations. We had Green Revolution. Then we had the Vision 2020 that you said 2020 that you have said we had another vision 2025. And now we're having this 2050 because these plans are just being put on paper and nothing concrete is being done about them. So that's why I am not excited. And the other reason why I'm not excited is that to be honest, the Buhari government should be writing their handover notes. Honestly, I mean, the Buhari government has got probably about three months left in office. This is a time that every department, ministry and agency of government from the highest to the lowest level, we should be making their handover notes. This is not a time for the Buhari government to start embarking on a plan. They could have embarked on the plan in their first year in office. And now that they have gone eight years in office, they should be telling us that, okay, the plan we set up eight years ago, this is what we have achieved. This is what we have achieved. This is what we have achieved. That's what they should have been telling us in the last three months they have in office, not sitting down in their offices, spending humongous money and putting a plan in place which the next government can as well just throw it into the bin. So that's the other thing that I'm not excited about. The third thing that I'm not excited about is that I have looked for this Nigeria agenda 2050 document online. I couldn't find it. So I was not able to even see the details or what's in the plan. We're going by what we have already said about past plans. I know that we make these plans without taking care of the fundamentals. There are fundamentals that grow in economy. I mean economic development comes from setting fundamentals. And the very first fundamental is the rule of law. The rule of law is what brings all citizens on an equal pedestal.  In the society that does not have rule of law cannot have development.  I know that, I mean, this policy has not been launched, however, is still, you know, in the working or proposed however it is. But, you know, one of the highlights of this plan or agenda is that it sets to transform the country into an upper middle income country with a significant improvement in the capital income. And you know, you know, the capital income currently for Nigerians. Yes. So that is a big question. The million dollar question is that how are we going to move from a low income country to a middle level income country and then to a high level income country? We have a capital income of $2,000 and the likes of Singapore have $30,000, $40,000. So how are we going to do that? And you see, there are basic fundamentals, like I was saying, the first that this cause, which is the rule of law, is totally absent as shown by the president this morning, comes from TV, totally disregards the ruling of the highest court in the land, which investor looking at that president is going to bring his money in this country and invest when he knows that the court in the land can give him the investor judgment and the president can routinely disregard it. That is number one. Number two, electricity. There's something called electricity. Electricity is the life blood of any modern economy. Without electricity, all your development plans, all the agendas, all the visions, everything you have in place is not going to work because with electricity, you are like a doctor who wants to heal a body without blood. Imagine a doctor trying to save a body, make the body to thrive, wants a body to flourish and do well and be healthy and there is no blood in that body. Electricity is the blood of the economy. And Nigeria, as we speak today, messy, is delivering 3000 megawatts of electricity to 200 million people. You know, the likes of Qatar with less than 3 million people, which is the less than the population of Abuja we are speaking from, is delivering 8000 megawatts. You know, so we just make these plans, but we don't take the steps to bring these plans to light. Look, if you give Nigeria 30,000 megawatts, if we move from the current 3000 to only 30,000, development will start coming to this country. The private sector will begin to thrive. You will not even know that this is Nigeria again. When you will see our very industrious people beginning to do things, beginning to manufacture, beginning to create jobs and all of that. So these guys just sit in Abuja. They make these plans, but they are taking no concrete steps. The other sector is steel, iron and steel. We have all the steel plants across the country that have been allowed to die. They are dead. Without steel, how can you develop? There can be no infrastructure. If you don't have steel, we are burning away our gas. And gas is the fuel for development. That is the fuel for industrialization. We produce it, we burn it. We are not putting it to use. So these are some of the pillars that activate development. We talk to you doing these things.  I have never even bought a jump form. You want to make a first-class degree in four years time and you have not bought a jump form. I'm going to talk about you enrolling in school. And that is the story of Nigeria. We're not taking care of the things that will give us the development. So 2050 will come and it will still go down the drain like 2020 or 2025. That's the way I see it, except for some changes. All right. We just have a couple of minutes to go. So I'll ask you to make this quite quick. What's your assessment of, because Messi talked about Vixen, 2020 which was put in place by a previous administration and when Buhari came in, following the recession that was on ground and continued in his administration, he came up with the economic recovery and growth plan ERGP 2017 to 2020. And when he inaugurated this steering committee in the year 2020 or 2021, he said that for this current plan, he said they had to replace or have a successor plan to Vixen 2020 and the economic recovery and growth plan. We may not be able to adjudge this administration, Buhari's administration on the Vixen 2020 since he didn't put it in place. But on the economic recovery and growth plan, which touted a lot, we kept talking about lifting a certain number of persons out of poverty, looking at a million development goals or which became the sustainable development goals and know that how do you think the Buhari administration fared with that economic recovery and growth plan? And how do you think that would affect how they will fare with this one if the APC wins the forthcoming election? Okay, yes. So thank you for the question. First on Vixen 2020. We are witnessing to either as a total failure. The vision said in the year 2020, which is three years ago, will be one of the top 20 industrialized nations. We're not even top 150. Nigeria is still at the bottom of every human development index. Every single one of them, we are counting the lowest. So that vision was just dead on arrival. When 2023, we can make a statement about it. It's a total failure. Buhari's vision as it came in is also a total failure. As you can see, everything in Nigeria has gone southwards. The inflation rate is going southwards. The foreign exchange rate is going southwards. Cost of petrol is going southwards. Unemployment is going southwards. Power supply is going southwards. Fuel scarcity is going southwards. Everything is going southwards. So whatever it is that the Buhari government put in their vision or plan has failed because of empirical evidence. We're Nigerians. We're Nigerians. We're experiencing it. If things improve, we know. But things are not improving. Reported in Nigeria is feeling the pinch. Feeling except those who have access to maybe a few subsidy money or they are round tripping the dollar into the power market. Those who are making money without lifting a finger. But for the rest of us in Nigeria, everybody is feeling the pinch. Yeah. I just saw the places on your table. We are out of time. We have to go. But the priorities of that economic recovery and growth plan, they said at the time, as of 2017, stabilizing the macroeconomic environment with low inflation, low inflation. They talked about using agriculture to achieve food security, create jobs and save foreign exchange on food imports. They talked about ensuring energy sufficiency, power and petroleum products by delivering at least 10 gigawatts of operational capacity by 2020. They said improving Nigeria's inadequate transportation infrastructure to support the economy and reduce the major cost and constraint of businesses. Okay. We know what happened with the airlines and how much we are paying. So I think this is just driving home the point that you are making that we just failed, really just woefully failed. Nick, thank you so much for your time. F9, coffee, it is F9, F9, F9 on everything you have mentioned that is part of that plan. F9. Nick, we have to go. We are witnessing it. We are seeing it. We have to go, Nick. Thank you so much for your time. Well, thank you so much. Nigerians, next week Saturday is the death. We are going to elect a new president and members of the National Assembly. Please, please, I need them for you. I need them. Please. Let's go and do this. Let's go and do this. 25th of February, next week Saturday. All right. Nobody should stay behind. Yes, we have to go now. Thank you so much. Nick Agoulet, we take a break and when we return, we'll continue with our conversation here. And for the second leg, we'll be looking at the issue of gender equality or inequality. Have a look at it. Please stay with us. Good morning.


time for the MacGeekGab and listener, Pilot Pete, that's me, brings you this week's quick tip. If you have an Apple watch and it's in the always on mode, it's muted, when you raise your arm and look at your watch as it comes to light, all you have to do is say 20 minutes and it will automatically start a 20 minute timer for you or you could say 1 30 p.m. and it will set an alarm for you at 1 30 p.m. I discovered this quite by accident but it works. Give it a shot. More quick tips like this plus your questions answered today on the MacGeekGab number 1004 for Monday, October 16th.


Okay, so let me have your attention you see we are now more or less you know comfortable with thinking of the point at infinity of functions behaving at infinity, analyticity at infinity, singularities at infinity okay. So you know we wanted to do that because we needed to look at functions on the extended plane okay and this view point is very very important because it is not normally when you do complex analysis say for example in a first course you are worried about only functions on the plane okay on the complex plane you are not worried about the point at infinity okay and but if you include the point at infinity you get more information that is the point. So I explained this last time but let me again repeat it, so I am saying for example look at let us take an entire function okay let us take an entire function take a non-constant entire function okay. Then if you look at the little Picard theorem what it will tell you is that the image of the whole plane is going to be either the whole plane or the whole plane minus one point which is one value which it may not take and that is the that is the best possible I mean it cannot miss two values what it means is that if an entire function misses more than one value it has to be a constant okay. So you see and of course you have but then you know if I ask you now take this entire function and take the exterior of a circle of sufficiently large radius okay and take its image what will the image look like okay then you know you do not have an answer you do not have an answer. So whereas for example if you knew that the that if you can think of infinity as and you know a singular point and in fact if infinity is an essential singular point okay then you can apply the great Picard theorem which will tell you that the image of every deleted neighbourhood of infinity will be either the full plane or the plane minus a point okay. So you can use that which is a more powerful theorem to say that if you have an entire function and suppose it is not algebraic namely that infinity it is a transcendental entire function that is infinity is you know essential singularity then if you take if you take the exterior of a circle of sufficiently large radius for that matter if you take exterior of any circle okay because exterior of any circle is going to be a deleted neighbourhood of the point at infinity in the extended plane and if you apply Picard the big Picard theorem you get the information that the image of the exterior of any circle is always is always going to be the whole plane or the whole plane minus a point okay and it will also give you the additional information that all the all the values it takes it takes on infinitely many times okay. So you see the you see the advantage of thinking of the point at infinity okay you get more information so so along these lines you know that you know for example you can characterize entire functions as transcendental or algebraic based on whether infinity is an essential singularity or not if infinity is not an essential singularity then it is a pole or a removable singularity if infinity is a removable singularity then it will by Lewis theorem the function has to be constant if infinity is a pole then the function has to be a polynomial and otherwise it is a transcendental entire function infinity is an essential singularity okay. Now what we need to do is see we are the whole aim of this all this is we are trying to prove the big Picard theorem and as a corollary deduce the little Picard theorem okay and you know theory required for that is to do analysis on compact spaces of meromorphic functions okay. So you have to study the topology and you have to understand do some analysis using compact families of meromorphic functions so we need to worry about meromorphic functions so let me so let me start by telling you what a meromorphic function is I have told this before but let us go into that a little bit more detail because that is something that gives you a link to algebra okay so the reason why lot of complex geometry is connected to algebra is because of the fact that all the meromorphic functions they form a field naturally and that field is an extension field of the complex numbers because the complex numbers always can be thought of as constant functions every complex number corresponds to the constant function given by that number so you know and constant functions are of course meromorphic okay they are analytic so you see that the field of meromorphic functions as a field extension of the complex field is the properties of this field extension in algebra for example in Galois theory and things like that that determine a lot about the geometry of the domain on which you are studying the meromorphic functions okay and this is extensively used for example in classifying Riemann surfaces and more generally if you want to classify manifolds and so on complex manifolds you can use this theory okay it gives you an interface between complex analysis and topology and algebraic geometry complex geometry okay and algebra in that sense okay so what is a meromorphic function the definition is pretty simple it is a function which has which is analytic on a domain okay but the only singularities it has are poles okay that is the definition of a meromorphic function. So let me write that down so the field of meromorphic functions so here is the definition let D in the extended complex plane be a domain okay so I am looking at a domain in the extended complex plane by mind you it means that it is an open connected set and of course we always assume that it is non-empty okay a meromorphic function on D is either an analytic function analytic function on D or a function that is analytic on D except for poles okay so meromorphic function by definition is a function that might that could be defined on D or D minus points where those points will be of course isolated they will be of course singularities okay and the point is that they have to be isolated in fact they have to be poles okay this is the definition okay so we say that we often use the abbreviation I mean we use this short phrase analytic except for poles that is the that is what meromorphic means okay and now we need to make a few observations the first thing is that you see the number of poles okay the set of poles of the function it may be of course empty in which case a function is actually analytic or holomorphic but if it is not analytic then it has poles at least one pole and the fact is that set of poles in D will be a countable set so the first thing is that you cannot have an uncountable set of poles so a meromorphic function will have only countably many poles and what is the reason for that the reason for that is because of second countability okay see the complex plane is just R2 and you know Euclidean spaces Rn they are all second countable because they have a countable basis so you can take all the open balls centred at points with rational coordinates and with radii given by rational numbers okay and use the fact that the rational numbers form a countable set okay and then you get this collection of open balls centred at rational points with rational coordinates and having rational radii as a countable collection of open sets and they will form a basis for the topology okay in the sense that any open set is a union of such sets okay and the intersection of any two sets like that of this type again is a union of sets of that form okay so it is a basis for the topology so the topology has a countable basis this is second countability and now in particular for example the plane R2 or the complex plane as topologically is second countable so you know what you can do is suppose you have so and of course any subspace of a second countable space is also second countable because you all you have to do is that you have to take the countable base countable base for the bigger space and intersect it with the subspace to get a countable base for the subspace okay so if you take the domain you take any domain in the complex plane or extended complex plane it will be second countable okay and by the way if you are looking at the extended complex plane of course it is homeomorphic to the you know the Riemann sphere and the Riemann sphere is a subset of R3 real 3 dimensional space and that and since real 3 dimensional space is second countable the Riemann sphere being a subset is also second countable okay so the extended plane is also second countable okay after all you are just adding one more point at infinity and if you want you can take all the discs centre at infinity but of course you should not say finite radius okay unless you are looking at the images in the Riemann sphere with the point at infinity corresponding to the north pole okay but in any case if you are taking a domain in the extended plane it is going to be second countable and now if you take a function which has poles in that domain then the set of poles the poles by definition are isolated poles are by definition isolated singularities so you have an isolated subset of a second countable set of a second countable space an isolated subset will always be countable okay the reason is because since the points of the subset are isolated you can cover each of those points by a member of the countable basis okay and you can choose different members from the countable basis because the points are separated from each other because they are isolated and in this way you get a mapping an injective mapping from the set of isolated points in this case these are the poles to the countable base okay and the moment you get an injective map what it tells you is that whenever you get a map from a set to an injective map from a set to another set which is which is countable then your original set is also countable because a subset of a countable set is countable okay therefore you see the first observation is that a meromorphic function will have only countable in many poles and then if you are looking at a meromorphic function on the whole Riemann sphere okay which means you are taking the domain in the extended complex plane often I keep saying Riemann sphere because I think of the extended complex plane as Riemann sphere they are one and the same so if your domain is the whole extended complex plane and you are looking at a meromorphic function on the whole extended complex plane you get more what you get is not only is a set of poles countable it is actually finite because an isolated set of points in a compact set second countable set is going to be only finite okay because you know one property of compactness is that if you had an infinite subset it should have an accumulation point okay therefore the moral of the story is that if you are looking at a meromorphic function on the whole extended plane then it should have only finitely many poles okay so let me write that down so here are remarks so remarks number 1 the set of poles in D is countable by second countability okay so I am just saying that I am just using the fact that the poles are of course isolated and I am using second countability okay and the second remark is that if D is the whole extended complex plane then the set of poles is finite and that is because of compactness of the extended plane okay and then there is yet another fact if you see the set of poles they form of course they are set of isolated points because poles are by definition isolated but on the whole some of them might converge see they mean isolated points but they may get closer and closer and closer okay so like the sequence of real numbers 1 by n okay the sequence of real numbers 1 by n consist of you know it is a set of isolated points but it converges it converges to 0 okay so you could have a set of poles okay you could have a convergent sequence of poles and then the fact is that this convergent sequence of poles has to converge only on the boundary it cannot converge in the interior. The reason is that if it converged in the interior you are going to get a point which has to be in the domain of f so it has to be either singularity or it has to be a point of non-singularity but then you know it cannot be a point of non-singularity it cannot be a point of analyticity because it is approached very as close as you want by poles and if a point is a non-singular point there should be a disc around that point where there are no singularities but since this limit is being approached by poles this cannot be a non-singular point it cannot be a holomorphic point or analytic point it has to be therefore necessarily a singular point but then you assume that the singular points are all going to be poles and here you have gotten a non-isolated singular point that is a contradiction therefore if the set of poles of the meromorphic function has a convergent subset then it will converge only on the boundary okay and of course this cannot happen if in the case when the domain is the whole extended plane because when the domain is the whole extended plane okay the boundary is empty alright and there are only finitely many points okay. So well so let me write this down if the set of poles has convergent sequence of distinct points then it has a limiting point in the boundary of T okay that point cannot it cannot converge inside T okay so you know the so the moral of the story is following the moral of the story is when you are looking at meromorphic functions and you are of course if you are looking at meromorphic functions on the whole extended plane then there is not anything we are going to see that these are exactly the rational functions okay we are going to prove that rational functions which are given by you know quotients of polynomials they are exactly the same as the meromorphic functions on the extended plane there is nothing more okay but if your domain is not the extended plane okay then you then the meromorphic functions if you look at for example if you are looking at meromorphic functions on the unit disc okay then it is possible that you may have a sequence of poles that is converging and it will converge to a point in the boundary of the unit disc okay and behaviour at that point of this of this meromorphic function or this family of meromorphic functions is very very important topologically okay so this is very very important that you need to study the boundary points also okay especially when you have sequence of poles tending to the boundary okay and of course what the remark says is that the if there is a sequence of poles which is converging it has to go only to the boundary it cannot come cannot converge to your interior point okay well now so let me go ahead with this fact that I told you that you know rational functions of meromorphic and the converse holds a rational function is given by a quotient of polynomials f of z is equal to P of z by Q of z okay. So you know now I want to tell you something I am now all this time you know I was using the variable w I was writing f of w g you know the reason why I was using the variable w is because I wanted to study the point w equal to infinity and the way I would do that is by studying g of z equal to f of 1 by z which is f of w by making the transformation w equal to 1 by z okay but now we have now by now we understand how to deal with the point at infinity so I am switching back to the variable z okay so z will be our complex variable from now on so rational function is just a quotient of polynomials so P Q polynomials in z with coefficients in complex numbers of course you know quotient of polynomials of course includes even constants okay you can take Q to be 1 okay constants are also treated as polynomials of degree 0 okay in fact in particular 0 is also considered as a polynomial constant polynomial and therefore you must understand that constants are also meromorphic functions okay and of course you know of course a function rational function like this is certainly a meromorphic function on the extended plane that is very clear because if you take a function of this form if you take a function which is quotient of polynomials okay it is going to where is it going to where is it going to have problems with analyticity it is going to have problems with analyticity where the denominators vanishes so you take the those point and where the denominator vanishes is just the set of zeros of a polynomial that is only finitely many points okay and maybe some of these maybe the numerator polynomial also has zeros at some of these points so some of these zeros may cancel out okay but then the fact is that this function cannot have poles at points more than the set of zeros of the denominator polynomial okay and at all other points it is analytic so it is an analytic function defined on the whole you know extended plane with having only you know finitely many points which are going to be poles so it satisfies the definition of a meromorphic function so you see therefore a rational function is certainly a meromorphic function okay and the fact the theorem is that the converse is also true okay and so that is what I am going to talk about rational function is analytic on C union infinity except possibly at the zeros of the denominator polynomial hence it is meromorphic on the extended plane so the theorem is that the converse holds the converse holds so here is essentially here is a theorem if f of z is meromorphic on the extended plane then f of z is a rational function okay so there is no difference between meromorphic functions and quotients of polynomials okay there is absolutely no difference and you know now this should you should now think of it like this you if you look at the polynomials in one variable in say in the variable z with complex coefficients that gives you the polynomial ring in one variable over the complex numbers C square bracket z okay and you know that is an integral domain if you have studied that in algebra and then this integral domain has what is known as a field of fractions a quotient field this is just like you get the rational numbers as a field of fractions when you look at the integral domain consisting of the integers okay so if you look at the field of fractions of the polynomial ring in one variable over complex numbers you are going to get just quotients of polynomials okay and these are precisely the meromorphic functions on the extended plane so the moral of the story is that if you look at the extended plane okay the set of meromorphic functions automatically is a field it is none other than the field of fractions of the polynomial ring in one variable over C okay so you can see that so well so let us try to prove that theorem let me use another colour so prove so you see so I am given a function f z the function is supposed to be considered on the extended plane okay which means you have also considered the point at infinity okay and then you the only information that is given to you is that the function is meromorphic which means you know that it has only poles and since the set in consideration is the extended plane is compact you know I have already told you they are going to be only finitely many poles okay and it is possible that infinity may be a pole or not okay so first let us first deal with infinity first okay and so you look at the laura expansion of the function at infinity alright and you know that the laura expansion of the function at infinity will consist of both positive and negative powers of z okay and of course the constant term and you know the singular part at infinity is the part that consist of positive powers of z okay and you know since so now you see infinity there are 3 choices for infinity see infinity can be either removable singularity okay or it could be a pole okay and of course it cannot be an essential singularity because we have assumed the function is meromorphic so it cannot have any singularities other than poles okay now if infinity is a removable singularity okay it means that the if you take the laura expansion at infinity okay the principal part which consist of positive powers of z or there is a singular part has no terms okay and if you assume so it consist of only the constant part and the negative powers of z okay that is if you assume infinity is a removable singularity if you assume infinity is a pole which is only other possibility then you know that the principal part of the singular part consisting of positive powers of z has to be finite so it has to be a polynomial of positive degree okay without a constant term and of course the degree will be the order of the order of the pole at infinity okay so in any case you are going to get the singular part as either 0 or a polynomial that is what I am trying to say at infinity and if you take the function and remove that singular part whatever is left is going to be analytic at infinity that is what you must understand so you see this is something that we use repeatedly what is the point about the laura expansion at a point of a function the laura expansion consist of a singular part or principal part and an analytic part and if you take the function and subtract the singular part what you will get is only a Taylor series which will be actually the Taylor series of the analytic function which is given by the difference of the function and its singular part the moment you take away the singular part the principal part the function that the function becomes analytic okay so this is a trick that you always use if you want to extract the analytic part what do you do you take the function and subtract the singular part or the principal part okay so let me write that down so let us first deal with the point at infinity the point z equal to infinity if the laura expansion of f of z at infinity is f of z is equal to sigma n equal to minus infinity to infinity An z power n that is sigma so let me write it like this sigma n equal to 0 to minus infinity An z power n plus sigma n equal to 1 to infinity An z power n z power n of z is this and now let me call this fellow as P infinity of z okay this P infinity of z is what this is the singular or principal part at infinity okay so let me so this is the this is the singular or principal part at z equal to infinity okay and of course whatever is left out here this is the this is the analytic part okay so you see of course you should take this laura expansion to be valid for mod z greater than r for r sufficiently large so it is so valid for mod z greater than r are sufficiently large so this is very important okay and so if you take so the point is that so if you take f of z minus P infinity of z okay this is going to be this is analytic at infinity okay this is going to be analytic at infinity okay because f of z minus P infinity of z will only consist of the constant term A not and negative powers of terms involving negative powers of z and negative powers of z behave well at infinity okay and of course I should tell you something if you look at the point at infinity since we have assumed that f is meromorphic this P infinity of z is not actually a power series it is only a polynomial okay P infinity of z will be 0 if infinity is a removable singularity that is a point of analyticity for f and it will be a polynomial of positive degree equal to the order of the pole of f at infinity if infinity is a pole okay so let me write that down note that P infinity of z is 0 if infinity is a removable singularity of f and is a polynomial of positive degree equal to the order of f the order of the pole of f at infinity there is no other possibility you do not have the situation when infinity is an essential singular point okay because we have assumed f is meromorphic the only singularities that are allowed are poles okay fine so now what you do is you look at now let us look at the let us look at the other singular points see I have assumed f is meromorphic so it has only finitely many poles because it is meromorphic on the on the external plane which is compact that is very very important okay there are only finitely many poles in the usual complex plane now I forget the point at infinity because I have already dealt with it I now want to keep track of the points on the plane where f has poles there are only finitely many let me call those points z1 through let us say zn okay so let us write that down let z1, z2 and so on zn be the poles of f of z in the complex plane okay and again let me stress this is very very important that you are getting finitely only finitely many poles because you are you have assumed that f is meromorphic on the extended plane the compactness of the extended plane is doing a big job here otherwise you need not get finitely many poles okay. So so you take these poles now you know you whatever you did at infinity you do at each of those poles okay so take any of those poles then in a in a deleted neighbourhood of those poles each of those poles f admits a Laurent expansion and you know if you take the Laurent expansion if you take the singular part it is going to have only finitely many terms okay and though and of course the highest negative power occurring will be equal to the order of the pole okay so so let the Laurent expansion of f of z around zk be f of z is equal to sigma does m, m equal to minus infinity and I will call the call I will call the question is a mk okay a mk and mind you it will be z minus zk to the power of m okay this will be the Laurent expansion the Laurent expansion centered at zk okay and valid in a deleted neighbourhood of zk and of course you know that will be actually a disc centered at zk and radius will be equal to the distance from zk to the nearest of the other zj's okay so valid valid in 0 less than mod z minus okay where of course rk I am not writing it rk is the distance of zk to the nearest of the other zj's j not equal to k okay and what is the principal part at zk it is going to have only finitely many terms okay and the highest negative power of z minus zk you are going to get that is going to be the order of the pole of f at zk so the principal part the principal part of f at zk is therefore pzk of f which is going to be let me let me write as pzk of z that is going to be sigma is going to be m equal to minus 1 to minus let me put tk amk into z minus zk to the power of m okay mind you where tk is equal to the order of the pole zk of f mind you these are all all the powers of z minus zk are in the denominator I am starting with m equal to minus 1 and going all the way up to minus tk and of course the a minus tk, k is not 0 a minus of tk, k is not 0 I mean this is the coefficient of the highest negative power of z minus zk right well so this is the principal part at zk and now what you do is that you do the same trick as before you use the fact that if you take the function and subtract away take away the principal part whatever you are going to be left with is going to be analytic because it is going to be a power series so it is going to represent an analytic function whose Taylor expansion at zk is exactly that power series which is the analytic part of the lower expansion see the law you must always remember this analytic part of the lower expansion is actually the Taylor series of what analytic function it is the it is the Taylor series of the analytic function which is given by the original function minus the principal part okay so let me write that down we need to use it f of z minus p zk of z is analytic at zk okay. So you see so now look at the look at the scenario the scenario is I have this meromorphic function f there are these poles finitely many poles z1 through zn okay and at each of these poles there is a principal part okay and if you take the principal part away what you get is something that is analytic at that point and of course there is also principal part at infinity okay. Now what I do is I take the function and remove all the principal parts okay you take the function, subtract the principal part at z1, subtract the principal part at z too and so on you subtract the principal part at infinity you subtract all the principal parts and what are you going to get? You are going to get an entire function on the whole Riemann sphere and what is it going to be? It is going to be a constant because of L'Huile's theorem. An entire function which is if you are going to get an analytic function on the extended plane which means you are getting an entire function which is analytic at infinity and entire function analytic at infinity by L'Huile's has to be a constant it is a bounded entire function analytic at infinity means bounded at infinity bounded at infinity means it is a bounded entire function and it is constant. So the moral of the story is you take the you take this Meromorphic function and subtract all the principle parts you are going to get a constant and now you push all the principle parts to the other side you will get that the Meromorphic function is a constant plus all these principle parts but each of these principle parts are rational functions and the constant is also a rational function so you have expressed the Meromorphic function as a sum of finitely many rational functions therefore it is rational and that proves the theorem okay so that is all. So let me write that down now consider g of z is equal to f of z minus sigma k equal to 1 to n p z k of z so these are the principle parts at those n poles and then also take away p infinity of z okay. Now what you get is g of z is analytic on the whole extended plane and by Liouville therefore it is a constant g is analytic on c union infinity hence a constant by Liouville so f of z is equal to constant plus sigma k equal to 1 to n p z k of z minus plus p infinity of z which is Meromorphic on the extended plane and that is the proof of that theorem that a function which is Meromorphic on the extended plane is just in fact what I want to say is not of course it is Meromorphic point is it is rational okay that is the point we wanted to show that a Meromorphic function on the we wanted to show that the Meromorphic function on the extended plane is a rational function okay. So what you have got is you have proved that a Meromorphic function f is constant plus these principle parts finitely many principle parts so this part p infinity of z is a polynomial okay it could be 0 and these are all involving negative powers of z minus z k's finitely many for each k okay and this is of course a rational function if you take LCM you will see that you will get a quotient of polynomials therefore it is a rational function and the beauty of this proof is that this proof also tells you that you get for every Meromorphic function you get a partial fractions decomposition the each p z k they are all the various terms of the partial fractions decomposition so this proof in one stroke tells you that a Meromorphic function has a partial fractions decomposition and is actually a rational function okay that is the advantage of this proof okay so I will stop with that.


Azure. You're muted. You have to unmute yourself. You can't leave me hanging out here all alone. There we go. Oh, there you go. I figured it out. Okay. Like, oh wait, do I need to do that? Well, hello everybody who's watching. We have a nice little group here. Everybody come to find out who won the t-shirt this time. It seems like everybody's been going gangbusters today. Am I wrong? It's crazy. It has been crazy. Crazy good. I know. So have you been, uh, been able to add a bunch to? Yes, I've been pretty busy. I've been working on Peasley's on my Peasley name study today this afternoon. Oh, nice. Well, I see that you're in 99th place. That tells you how much everybody's doing. I know. You have a total of, um, 51. So you're ahead of me, which is how I'm going to be. How are you doing? I'm in 113th place. I keep falling down rabbit holes as usual. It's like, I'll start going here and then all of a sudden I'm going this way and that way. And then there's this guy over here and you know how that goes. And then you find something really interesting about this one person and you're like, what is that? Exactly. I came across this one family where everybody had married at least twice. Oh, wow. Yeah. Everybody. I don't want to add all those extra spouses. I want to learn more about these people. So it's hard to just, I don't, I applaud those of you who can just dive in and just add, add, add, add. I can't do it. I tried. Yeah. I found this one piece, Lee, relative that all I have for a death record for him is the military headstone record. Oh, yeah. That's all I can find. I can't figure out. Anyway, but yeah. So I've, that's another fun part about adding people, especially if you're working on your own family life is watching that. You see seven number go up. Yeah. Connection number. I wonder if your guy died over a seize or something. Yeah, 1944. So I bet he was in Europe or something. Yeah. So this is like, divorce lawyers must have made a fortune. I'm thinking, yeah. Yeah. It was such an unusual time for people to get divorced. What period you're working on? Well, it, this was like in the early 1900s up through the, oh yeah, in 40s.  Yeah. Lisa said that Greg checked and I was adding profiles during, I was, I was eating my sandwich and eating and, and adding stuff. So I told Mindy, I said, my son just brought me lunch. So I'm not going to make it. Poor Steven Tibbets has a slow internet. That is so frustrating. Lisa Murphy says she's had at least 20 connections from somebody that she started on. Wow, that's the end yet. That's kind of fun when you keep expanding one family. Yeah. Oh, and her, she said her, didn't her CC7 went up by 48. Wow. That's awesome. Have you checked yours recently? I haven't. Let me just double check here where I'm at. I know. Wow. I was like at 2777 yesterday and now I'm at 2855. Nice. Yeah. I think I went up by about 17, something like that today. That's cool. I need to go back and work on my own list for a while. When I was first starting at WikiTree, I, one of the things I wanted to do was get my, you know, I have eight brothers and sisters married multiple times. And so one of the things I was trying to do is get their spouses lines up so that my nieces and nephews would have. Oh, that's nice. And so that's why I have so many now because I already had done a lot of the work before. Okay. Right. Your CC7 number is just up on your My WikiTree menu. It's the third after badges connections. Would you like me to show you on mine? I can do that because I know some people haven't found it yet. Let me see. Share screen. I project Italy people and Western Red Seeders people. Hello. I see y'all say hi. I can't share screen. I'd have to do, I'd have to do permissions again. I'm not going to take the time to do that. You want me to do it? I can share mine. Yeah. Okay. I don't know why I don't have permissions to do that on here. I need to go. Did you maybe do an update or something? I must have. Yeah, I must have. Okay. Okay. So let me go. You can add that, right? Yep. Can you see my screen? Is it sharing it? Nope, not yet. Okay. Do I need to add it here? Let me add it to the stream. There you go. Oh, there we go. Okay. Yeah. Yeah. The tunnel of infinity. Okay. So just right up here on My WikiTree. And it's the third item right here. It's all ready to go. And if you click on that, it takes you right there. And you have your, gives you your first setup of the degrees and how much for each degree. And you're all good to go. It's also on your profile page, right next to like where your contributions are. Yeah, right up here, right up top. Okay. Now hold the phone. You had a different thing on your connections that I have. You got a little table up there. What was that? Oh, it might be the WikiTree B. Yeah, probably. App that I have. Yeah, I don't have that on mine. Yeah. That's a little bigger. And it has the buttons for missing connections and a table and all that kind of stuff with the WikiTree. WikiTree does that. Okay. Yeah, a little extra. I can't remember why I didn't install that. I have so many extensions right now that I just, I think I just didn't want to add one more. So yeah, I got you. My mom has totally got me beat. She has a gazillion. She has almost, let's see. Oh, she's got 3,752. My gosh, that's awesome. Yeah. So anyway, okay, so that's how you can get there. There you go. So keep an eye on it, Kay. Oh, I see Eric is saying that it updates every 24 hours, but I believe that they're doing it more frequently now. Yeah. It's been happening like every time I go to my menu, it's like an updated number. Right. It's happening a lot more sooner than that. I think, oh, he's trying to get to the help page. Hold on a second. I think during the connectathon that they're updating it more frequently, which is awesome. It's like, it keeps you motivated. It does. Let's see, where and when counts appear. They're recalculated for all members twice every hour. So when you add family members, your count will be updated within 30 minutes. Nice. So it's not just for the connectathon. I think they boosted something so that we could get more updated info from that. That is awesome. Oh, Morgana, it's that CC7 number is people that are connected to you. So if you've been adding profiles, it wouldn't be that the number of profiles you've been adding. It's just if you're connected to them. Right. So it's like your, it's like your circles, like your first, second, third, fourth, fifth, sixth degree, and then this is the seventh degree. CC7. Okay, what does that, I'm something connections. I'm drawn up like what it stands for. Help me, you guys. CC7. Yeah, I don't. Connection, it's just connection counts. Of course it is. Oh, connection. Yeah, something simple. It's too easy, just too easy. Oh, that's crazy. So I think it's, you know, anybody within seven degrees of you, I guess that goes by marriage too. Yeah, it does. Yeah. Yep. So it's kind of like the Kevin Bacon thing, but they stretched it out to seven degrees. So yeah. And those, those badges we have now, 1000 sticker, the 2000 sticker. I have a ways to go to get the, I've got the first two. I need to go a little ways and get the second one or the third one. It's 5000. So. Oh, is it that, that's the next level? Yep. Cool. Like, why can't we have a 4000?  So are you guys wanting to hear some statistics? Let's do statistics. Okay, let's do, do we have a preference for what we want to do? I haven't caught up on all the, all the previous live casts. Does anybody have a preference for, I don't know what they did last time. I know I think Greg, the first one, Greg did like the teams, I think. Okay. From bottom to top. So whatever you want to do. Okay. So I guess I'll just do the first person on every team. How does that sound? Excellent. Sounds good. Okay. So I'll start at the bottom and work my way up. We got Musty Dusty and we have Deborah Allison with eight. And those are the profiles that are those older profiles. So this is, yeah, the hard ones are really hard work. Goes into those. Team Massachusetts, we got Ellen Smith with five. Van Yintree, this is a new team with the India profiles. And we got Rob Wilson with 25. Wow. Southwest Sunshineers, Gary Hackinson. Is that how you say that? Sounds about right. Yeah. 40 for him. South African spring box. Sonja. Sorry. Don't know how to pronounce the last day. 62. Oh yeah, that's a tough one. Hoyle, maybe. Okay. And then Irish idols. We have Feargal Hennigan with 58. And Little Team on the Prairie, Randy Zercher with 42. Welsh Dragons, Hilary Gadsby with 49. And then we have Mid Atlantic US with June. She has 25. I think it's, is it, how do you pronounce her last name? Butka. Butka. Okay. And then title in tortoises, Linda Sherman. She has 43. Northwest Terriers, Beverly Swan with 73. Twisted Thistles, Jean Scar with 79. Caroline, Canadian Connectors, Marilyn Assel, like Kassel without the C. Yeah, you pronounce that. Assel or Astley? I don't know. Astley, 90. I hope they'll come connect, correct us when we get them wrong. Yeah. Mid Atlantic, Part 2, Randy Breneman with 169. Oh, broke 100. Wizards of Oz, Nigel B. Clark with 65. And then we have Western Red Seeders. Yay. Patty Lapland has 184. And our team looks like our team just went over 500. Awesome. Great job. Okay. So all of the rest of these are above 500 for the teams. Nor'easters, Nanette Pazuti is at 69. Nordic Moir, Mark Williams is at 75. Legacy Ayres, Carol Stratton has 87. Flying Dutchman, Hank Lynx with 199. He's almost got 200 there. Yep. I think I'm going to refresh my thing here. How good idea. Yeah. Okay. So Team Missouri, Lamira Morton has 129. Germany Genies, Carrie Portlands with 302. Wow. Kiwi Crew, Ruth Ogilvy with 246. Mighty Oak Branches, Allison Palmer has 163. And Team Italy. Yay. Danita Zenre. I hope that I pronounced that right. Sounds right. Gangbusters with 438. Cornbread Catchers, Jim Loden has 550. He was describing in his member of the week interview what he does. That's amazing. Oh, crazy. Okay. Mighty Oak Roots. Caitlin Emmett, 164. Tree Nuts. Yay. That's your team, isn't it, Julie? It is my team. Jody Rogers has 403. She's been on fire. Emma is on Team Roses and she has 403. Oh, they're tied. Oh, did I see? Oh, Caitlin has 164. Sorry. I must have scrolled Tuzu in there. Oh, no. Oh, no, they are tied. I just get it right. Okay. Jody and Emma are tied. Emma are tied. Wow, they're battling it out there. Okay. Pip is on Southern Supersweepers and he's got 206. And then Virginia Connectors. Sandy has 456. Oh, I see. I just refreshed. She actually has 463 now. Oh, my goodness. I know. Okay. And I just refreshed.  Oh, my gosh. Great job, everybody. I don't have the comparisons to the last one. You know, like, where were we at this point on the last one? We have fewer people. Yeah. But we have a bunch of people who are really cranking them out. So that's pretty cool. This is awesome. Yeah, this is very cool. Yes. Looks like Jim Loden is leading the pack right now with his 550. Yep. That's crazy. Yeah. Oh, crazy, crazy. So much fun. So much fun. Good work. Nice job. Should we talk about t-shirts? Oh, yeah. We have a t-shirt winner. I hope she's still awake. Here she comes. It's Allison Davies from Mighty Oak Groups. So Allison, if you're listening, you'll get to, I think, I think you might get to pick a t-shirt or a mug and Mindy will be in touch after theathon is over. Mindy or Ao1. I'm not sure which one's doing that these days. But they'll be in touch. You don't have to go claim it or anything. I should write it down though so that I don't freeze to tell them because we would be sad. Oh, Mindy's here. She's probably already written it down. Yeah. Mindy, you have to get it because my pen stopped working. No, I've got it. Mighty Oak Groups. I will add it to the spreadsheet. I'm sorry. Go ahead. Have you come across any different kind of names, strange names out there yet? Not this time. Not so much. How about you? Nope. The one I'm working on right now is a little bit different. Verdel. Haven't ever heard that name before. Are you kidding? I had one today like just a little while ago. Yes. Verdel Adelaide. I can't remember what her middle name was. Now you're making me curious. I got to go look. That is so funny. Isn't it?  Oh my goodness. Was it V-I-R? V-E-R-D-E-L-L-E. In the last one, it was Trimble. Verdella May was mine. Wow, that's crazy. Verdella May Staver. Yeah, I love those weird, those different names because you read across records. You're pretty for a certain area. You're pretty sure. Yeah, I love it. Whenever I go through a family like that, I always look for the one child that has the weird name because there's always one, right? Yeah. Yep. You know what? I didn't mean you, Azure. No, it's true. It's true though. It's like, you know, all my brothers and sisters have regular names. Just like Bill and Tom. Yeah, Danny, Bonnie, Debbie, Terry, John, Naomi, Sean, Carl. Those are all normal kind of names. Yeah. Azure. Azure. But it's so pretty. There's a lot of girls with my name. Really? They were born about the same time as me. I did not know that. It's from a TV show, Kojak. Oh, I don't, I didn't make that connection. Yeah. That's hilarious. Anyway. But yeah, that's why I love it when there's a name. Yeah, because if you can start with that one that has a different type of name like you were saying, and there's like an obituary or something, you find that name and then you can kind of go from there. Definitely helps. Yeah. Susan Andrews says, but the weird names get misspelled so often. Yeah. True. Very true. And I've run across that exact same name, Susan Stamper and Stamford. Same thing.  Did you see that up a little bit further? Iva Alfanetta. That's a different name. Wait, where did it go? Oh, yeah. Wow. Susan, yeah, that's different. That is different. And then there was oddly, oddly Lawson. That's kind of mean phonetically. Oddly. Yeah. Yeah. Okay. Crazy. You've got any other good ones you guys have to share. There's Anne says she has her sisters. Is it Chandra or Chandra? I'm curious now. Yes, and our very own Aowyn. Yeah. That's Chris points out. We're so used to her name now it doesn't shock us anymore. Yale Saville McCartney. Wow. That's an interesting one. Alvie. Oh, yeah, I've seen this one all the time. We have the mother's maiden name is the middle name. I love that. Yeah. I do too. It's helpful if you know that that's the case. But I actually had one where it was her middle name and I screwed up and thought that it was her maiden name. Oh, it was just I made a mess. I didn't make a mess but I had to do a little merge. So. Oh, her grandmother. Chris has to explain this. I have no idea what he's talking about. To you. Yeah. Is it Captain America or something? Yeah. Okay. And when he was born. Yeah. Oh, Micah, my grandmother's name is blue eyes. No way. Like blue is her first name and her middle name is eyes. Micah, fill us in. That's interesting. And Chandra. Okay. Liza, Gervay. Is it Lisa or Liza? So you have, I think I remember you talking about that during a previous fun. Do you have to share? Oh, I had, I had one. His name was Hank. And, and so I was looking for Henry, but then I found his birth certificate and it was something like Hankison, Hankinson. Whoa. Yeah. H-E-N-K-E-N-S-O-N Hankinson. Wow. Yeah. Oh, yes. Liza says it's Liza.  That's so funny. That's neat. That is neat. Oh, do you see Mindy's? I do. Micah. That is so cool. That is. I love that. That's, that's an attractive thing. I can't say it's pretty. It's her nephew. All right. Oh, Skeffington. Well, I don't know what there, what it is about that name, but I like it. Skeffington. Okay. And I know that I probably mispronounce Cohen's name all the, wrong all the time. So, because he comes into Friday, date nights, Cohen, can you spell it phonetically for me so that I don't do it again? Oh, so we're just going to sit down. Yeah, I was always wondering about that, too, whenever I saw his name, too. Yeah. Oh, this is funny. Liza's uncle Russell H. Macklin Jr. was always called June for Jr. and I've, I've run across a bunch of men named June in registering research. It wasn't probably for Junior, but okay. So, Coon, I don't need to do the, what do we call that, the diphthong in the middle. It's just Coon. K-O-O-N. Okay. I will try to remember and I will try not to mispronounce it next time. Thank you. And Eric's grandmother's first name was Dovey. That's cute. That is neat. Yeah, I have a great, great grandmother, Lovey, the name of Lovey, her first name. They could have been twins, Lovey Dovey. Oh, no, I've never seen men named Judy. Me neither. Wow. I ran across a gale today that was a man. What's the other one that I've seen more recently that? I had a rubin that was showing up as a ruby. Oh. You know, as a, as a nickname. Yeah, I could see that. And I suppose once you know them, that's not, that doesn't seem unusual. Yeah. You know, once you call on that for a while, it doesn't seem unusual, but it does seem like it should be a woman's name. All right. Shall we let them get back to work? Yes. Everybody get back to work. Crick a lip. I had to take a little break. I was getting all bleary eyed. I'm like, I gotta go do something different. So yeah, so now I'm ready to get back in there and dive in. All right. Okay, everybody get back to work. Have fun. Yeah. Glad you guys popped in. We will catch you in three and a half hours. So bye. See you then. Bye.


Hello and welcome to another minimal Godot tutorial Unlike the previous videos so far in this tutorial where we started off with a fresh Scene each time we're actually going to build on our last scene because we're just going to make some changes last time We created this little script here I can hit f6 to run this again There's a link in the description to my get lab page where you can get all the scripts and the assets But I can use my arrow keys to move my Player around here, but that's just the arrow keys. What if I want to use WASD right now? They don't do anything Now I could say if this button press I can give a specific button or that button or this, you know key or button or whatever But that's not a very good way to do it. Godot gives you a very nice way of doing it Let's go up to project settings here And the second tab over is input map and here you can see all the default inputs But you can also create your own input actions if we scroll down you can see here that we have ones for UI left UI right UI up UI down and you can see that there's in them They each have a key which is the left key on your keyboard So the key is for keyboard we got right, but you also see that they have device zero, which is going to be a game pad or joystick and you can see that saying button 14 which is by default on most key Gamepads is going to be left this one's 15. So we're able to link a bunch of different inputs You can create your own so I can come up here action. I can say move up I can say add and then down here It's been added to the list and I can press this plus button and I can add in a key from the keyboard a button from a joystick game controller or if it has a Directional pad that is pressure sensitive you have your joystick axes here or mouse input I'm gonna say key and I just press the key. So we're doing up. So I'm gonna hit my up arrow I'm gonna click okay, but now I'm gonna add another one I'm gonna hit key and I'm gonna hit w so now w so up and w on the keyboard both work for this If I go back to my code here, I can come in here and I can say and Should auto-complete for me when I start typing we have now in this list move up I can choose that I'll hit f6 to run this scene and You can see I have an error here. Let's go ahead and look at this You will tell you right down here when there's error. I forgot when I back spaced I forgot to put my colon here at the end of my if statement Okay, so now I'm going to hit F6 and now I should be able to hit up and he moves up or w and he moves up Down arrow still works, but we never say anything for s, but I could but let's go back into this and instead of Making that move up. I'm going to say Back to the UI up Don't forget my colon there I'm gonna go back in here project settings and if I want since I already have that set at any point I can add keys so for UI up. I can say add key W. Okay for right. I can say add key D. Okay for left. I can say add key a Okay, and for down I Can say add key s? Okay, so now with our original code here for UI right UI left UI down UI up I can use a game controller because that was already preset But if I start the game, I can now use either my down arrow or s I can use right arrow or D a Or left arrow or W or up arrow and you can add as many keys or button inputs You want to that and that keeps your code nice and short I don't have to say if this key or that key or this button or this mouse So that is how you can make your own custom input actions. Thanks for watching visit my site films by Chris comm That's Chris the K should be a link in a description as well as a link to the get lab page where you can get this project Thanks for watching and have a great day


news update. Good afternoon folks Steve Rhodes coming to you live from the shores of sunny delray beach florida this year 1pm update and currently have all the us indices that we track trading to the upside the dows up 373 points a little over 1% s and p 1 1 quarter percent or 52 points nasdaq 101 and two tenths percent 149 points Russell 2000 a half a percent nine points there the some eyes about a half a percent six tenths really 17 points the upside golds off 16 bucks that's nine tenths silver's down a quarter of a percentage that's six pennies out there lights recruiters off 65 cents you've got natural gas up 22 pennies a 30 year treasury tradeout 141 29 that's off 17 ticks out there let's go take a look at our nine panel market update chart we begin by take a look at the ES mini that's in the upper left hand corner would we know about it well one yesterday price closed below the bottom of its weekly profile that's a level to be watching come friday that's at the 40 where is that that is at 41 89 price also closed below its TD nine count breakout level that's a daily TD nine count breakout so that suggests lower price now it's native be equal CD to the downside a bullish reversal candle would generate a by the d-point spot follow tunics next panel that's still above its 50 day expense moving average that's always problematic for the S&P 500 the ES mini the NASDAQ and then this I've got to figure this out because on one system I've got the NASDAQ closing below the lows from the lows from arts the 14th 15th that is and that was a roadsman to indicator bottom but on this set of charts here shows that it's held but it just may be the synthetic symbol that I'm using here so I'll try to get that figured out during the quick break between the one o'clock update in the show out there nonetheless if we take a look at what the NQ also has native be equal CD to downside so really a bullish reversal candle would confirm a by the d-point the US dollar index that is trading higher I can't recall if I believe we're gonna have a TD nine count pattern that should complete between today and friday out there gold is failing to hold its TD nine count breakout level 1895 60 the next level support for it would be down at the 1873 30 level that is the bottom of its weekly profile silver is holding its breakout level that's at 2348 it has native be equal CD to the downside bullish reversal candle would also confirm a currently by pattern here lights we prove just ready between trend line resistance and trend line support natural gas fighting resistance at the top of its daily profile seven dollars and twenty three cents folks stay tuned for the creator said show draft start for a wednesday have a wonderful and thanks again for joining the reality