What is 0 to the power of 0?

Let's think. Where are we? What was the first thing we started, under indexes,

power

s, exponents,

what

is the definition of an index? If I wrote, you know, to the

power

m,

what

does that mean? It means a time sometimes, how many times? M times, right? Well. So we really write that. It is sometimes. I do not know, for many times, m is, correct, but it was one or five or 60, whatever, correct, so I will write that that is once that is what a and the power of m rather, that's fine, so we took this idea and said looks, we can build on this.

Good? If you have two numbers like this to m and to some other correct base, so this is what we write and if you multiply them to each other, you could rewrite it like that and tell it, but that took an eternity. Instead, we write. What do we call an index law, right? It is equal to that base and what is power? What do you do for a living? When when you multiply, you add the indices, right? So it is m plus n case, they are bells. Yes, okay? Exactly in the same way as if I divide in this way, the indices are subtracted well, you take the difference, so far everything is fine and then one of the most important things we deal with was that if these two numbers are the same m and n correct to the m divided by A to the N, you have a power of 0, right?

But then we said well that it must be 1 that must be one. That was the last "more", if you wish, that we established, so there are 1, 2, 3 laws, then we raise this question, agree? We said for any number the power of 0, it is 1. in the same way that you know that I can put this on side 0 to the power of any number that is 0. right? 0 square, 0 covered, 0 to the power of 100 ... 0 to the power of are you paying attention waiting for what? (Student :) I've been waiting for you ... I've been waiting for you. (Master :) Great. Thank you. (Student :) You're welcome, so, have you asked the power of zero?

Oh, well, yes, what happens when you meet them, right? Any number of power 0 is 1, anyone 0 The power any number is 0. So what happens when you together? Ok? now! Yes, there is a question now, this is where we will do it, and you will need your calculators for this, in fact, in fact I will get mine, we will also need everyone's calculators, so I will ask you to help me make some numbers, agree? So get your OK calculator. So here is the thing, right? If you look from this angle, if you are approaching this type, you would say that it should be or if you come from this direction, you would expect 1, then is any of those or is it something completely different?

Ok, this is what we are going to do, I'm going to draw a table. You. You don't need to draw this table, but you will help me fill it, okay? Mmm in what I want us to think is what these numbers are the same if I'm starting to approach ... you know ... really small numbers. So I have really small numbers. So, if you want, what we are about to do is something called limits, I will explain it shortly, but it seems that you know, right? And this is what you need in your calculator. In the middle in the upper part there is an ignition button, is it okay?

It looks like an X with a small square stuffed in the corner, okay? So, if you write that, for example, if you go, let me light this ... If you go seven, then press that ignition button to the right and that small box will appear, so this is what I wrote, it's fine. 7, then I will write that X with a box now if we write something like 3, so now three appear on the right of the power, so seven is the base and three is the pound that you press equal and get 343. Well, if Seven Cubed is 343, this is what we will do.

I want everyone to have a lot of different numbers, okay? So the hands to the hands, who has an adequate calculator like no other phone in a good good? So this is what I am going to do: I will write a series of things well and then I want us to solve what its value is. Well? So value and mmm. I am sure that all this will leave that plain. I will think of a bad name in a second good, so really important. We do the, um, the calculations with your calculator, so lift your hand again so you can assign some numbers, agree?

Everyone raises their hand so you can see well ... it's fine. Jag, you get the most difficult, do you get one of one's power? Keep your hand high Kyle will get 0.9 to the power of 0.9. (Kyle: Okay for me, yes) Okay, Jack can do 0.8 to the power of 0.8. Do you see what I'm going well? Tom - .7. Was it okay, okay? Very well, let's start from the top and remember again three decimals well, Jag be sure to read it carefully, do not miss any detail. What did you get? (Jag: 1) One but somewhere decimal? Well, then I'm going to Zero Zero Zero, okay?

There you have. Alright! Kyle, the following! .9! (Kyle: 0.909) 0.909? Ok Good Um, the next point zero point eight three? Seos eight three six, well, well, seven seven nine, it's fine. I want to pause for a second before reaching the number of Lucas, only looks for a second and take a look at what is happening, just take a look at what is happening, okay? I am trying to establish a pattern, can you see the numbers again? But trying to reach this correct, try more closely and close at this point if I had to guess at this point, what did you think we would happen when we reached zero?

How does it seem to go to zero? They were falling ... hmm ... well, let's move on! Who is doing? Lucas? Lucas: 0.736 0.736 is fine, who is the next one was - Nelson - Yes? Nelson: Zero Point Sev .. Amm Nelson: Seven Zero Seven. Okay, it is fine now for Bill *Bill begins to murmur well, well, now we will pause there for a minute to the next number that the people who suspected before now should have been even more suspicious because the numbers are decreasing correctly, but does not look at these correct types. They are getting close together. They are decreasing, but they are decreasing the speed, yes, that is correct.

Well, we really call that is exactly what it is. We call this exponential growth, but what we are seeing seems to be an exponential decomposition, but anyway, that is an assignment becomes even more interesting, who had point three, yes? 696 696 ... What?! What happened? Why am I decreasing speed, is not even slowing down? He has gone to the other side! Turn around. Well? Let's move on! Point two (0.2) wait ... two four ... we are going up again. We are going up. Well. Chloe forward Cloe: 0.793 is fine, now this is interesting that I am approaching. I know I'm getting there, but I'm number one.

I am not there number two, you see how here we were decreasing the speed, right? These holes are becoming very small, but now that I gave the gap they are getting bigger. Look, that is that gap as point three this point like point seven correct, so what is happening? Well? Now? We need more numbers, so we need your calculators again here the numbers. I will suggest that we go. We get half of this. What is half of point one? Think that it is .05, isn't it, Jarrod, they took you out when you do one to the power of one?

So why don't you do 0.05 to the power of 0.05? Well? Um kyle. Do you want to do it? We are smaller again. Let's .02 to Power 0.2. Well, Jack, joins 0.01, okay, I will tell you which one in a second Jack can tell me which is yours jarrod: 0.860 zero point eight six zero hmm still in the kitchen increasing yes Kyle: 0.924 0.924 still increasing yes jack: 0.954 zero point nine five hmm well is fine, now this time I go to zero, but in smaller chunks, but in small OK? I want to get faster. Well, this time, Tom, what I want you to put is and other people can see if they get the faster answer feeling smaller in Zero Point Zero One Ok, okay?

What do you get? Yes 993? Well, let's go again. We go ten times smaller again 0.0001 to the power of 0.0001. What is the same? Do you have it Lucas? Yes, yes, ah, now just because we have hit nine. What are the - out of curiosity - What are the other decimal places? Okay, okay, Ali Ali, can you do next time we are going? 0.00001 That is four zeros, and to the power of the zero zero zero point zero and a YEP. Four zeros one yes, four zeros, and then, what do we get? And I will need more decimal places this time, what happened to rest?

Ah, you missed a 1 there, oh, return to the beginning of good, mathematical error What did you get zero point? Yeah? I am (reading the number) is fine. I will go there. Yes, okay, five zero is five ... I'm sorry, one two three four five? Okay, it's okay signing at the point, well, now. This is interesting if I'm right if you can go far enough with your calculator. I think you will convince your calculator and then reach one. I suspect. Well. I can't well, you can sit, you can try to try it, but can you see what we have done two things, agree?

First, we saw it fall, right? But then he turned around, he began to increase like this, but then he did not increase forever. , really, did anyone get how many I have to put? Use. Can spam that you still go to your ranks until it is fine? It does not have that it does not have a notation, so one and also the 9 do not repeat forever, there are other numbers, so you cannot use a repeater well, so, therefore, we never reached 0 no 1 0 but the well. Nor is it so, but the best definition you get like what seems to be to the one who leaves is that it seems to 1 okay?

That is the best we can say, but I don't bother me, yes, well, it is seen that it begins to break down if you go more because with negatives. It does not work well, see that here you have to answer. This is an answer that we decided the numbers and the beginning of our definition, why makes the deepest in this context well, let me finish it by returning to this idea of ​​what everyone is doing with your calculators is called to take a limit? There is this idea of ​​this thing that approaches a certain number that we can never get there, but you can get close, so if you are the curious guy, you can write this and you can surprise your friends, okay?

It is a bit of strange notation, but I will explain what it means in a second. You must write it, then this looks like this, this, what does it mean that or does it mean to see this well? It means that x is approaching 0, you can see that error x goes there when X is closer, more and closer to 0 What happens ... with ... this guy here? This ... that to the power of yourself and the answer is that it goes to that! That is what he does, okay? He never comes there, but that's where he could get there.

That is what happened, okay? So I hope you give you a conclusive answer, so, if you go and look up on the Internet, which I know that some of you did. That is why you will find that this is the conclusion. Yes, you mean, why does it turn here? Now, that is a good question, and I don't have one answer at least, I mean that I don't have one right probably because I haven't really thought so much about that to be honest, I wonder, I mean there are always reasons for everything. So maybe we could find out where they are going