Good morning. Can you all hear me? Also from the back. Good, so welcome to the last class of our Ergodic theory course. So today we are going to put together what we learned from Stefano's class and Lucia's class and the background we've heard from the first two classes. And we're going to discuss Birkhoff Ergodic theorem, which is kind of the starting point of one of the fundamental results in Ergodic theory. So before doing that, let me start by recalling a result we've seen in the second class of Corinna's course, which is this theorem, which was due to Vile, that says that you fix any rational number alpha, then for any continuous function f on the circle for any x in the circle, then if you take the average up to time n of the values of the function f along the orbit of the point x by the rational rotation by alpha, and if you take n larger and larger, well, this in the limit converges to the integral of f with respect to the Lebesgue measure, so by lambda I'm denoting the Lebesgue measure. And here, let me stress that this holds for any point. So the picture you should have in mind, again, is the circle 0, 1, then you fix a continuous function f, and then you can pick any initial condition x, and you can look at the orbit of x up to time n. So a long segment of the orbit, so this is x. Say this is our alpha of x, our square alpha of x, and so on. And you look at the values of the function along the orbit, and you average all these points you get, and if you take a longer and longer segment of the orbit, well, what you see in the end is the integral of f. Is this clear? This we've seen already. So yeah, please stop me if you have any questions. Don't be afraid to ask. And let me add something else that wasn't stated explicitly, but if you look back to the proof of the theorem, should be clear, is that more precisely, not only this convergence holds for any point in x, but is also uniform in x. So the sequence of function, let me denote a n of f at a point, and this is just the average. Up to time n, it's composed with r alpha to the k of x. This is a sequence of continuous function on the circle, and this converges uniformly to the integral of f. And hopefully we'll see. I'll come back to this part later in this class. Anyhow, this is the kind of result we are aiming for. So we want to do something similar, but in our setting of ergodic theory. So what is our setting? In this class, we have, as usual, xb mu, which is a probability space. So by this, I mean that xb is a measurable space, and mu is a probability measure. Let me stress that it's really fundamental that the measure is finite. We've already seen a few times what goes wrong if you take an infinite measure. And again, so this is a measure space, so a priori, there is no topology whatsoever on x, so no continuous function, nothing. And then you consider a transformation t from x to x, and the only assumption you put on t is that it's measure preserving. This means that the push forward, t star mu, is equal to mu. And again, this map t, as what there is no topology, so it's not continuous, it's just a measurable map which preserves this probability measure. So we want to kind of do the same thing. We have x, and we want to look at some function f from x to the real, and try to do something like this. But the first question is, what assumptions should I put on f? So in this theorem, we're looking at continuous functions, but here we have no topology, so we have no way of saying what a continuous function is. So the first question is, what is the good class of functions we want to look at? Well, if we are aiming for something like this, and we want to take some integral, maybe we should ask at least for the function to be measurable, and we want the integral to be finite. So a natural assumption on the function is asking to be in L1 of mu. So is it clear what I mean by L1? So Lucia briefly defined it at the end. So this is actually a space of equivalence classes of functions, which are integrable and the integral of the modulus is finite, and you say the two functions are equivalent if they coincide almost everywhere. So these are the assumptions you have. The probability space, a measure preserving transformation, and L1 function. You want to pick a point x in your space, follow the orbit, so here you have T of x, here you have square of x, and so on. And you want to look at the average of the values of the function along this orbit, and the question is, these averages, let me call them again a n of f in one over n of x, do the averages converge? And I mean, what does it mean converge? So in which sense do they converge if they do? So do they converge point-wise? Do they converge in some norm? Well, it doesn't make much sense to ask them to converge everywhere because f is an equivalence class of functions, so if I change the values of f along a zero measure set, this is the same function in L1, so it doesn't make much sense to ask for these averages to converge everywhere, right? So in which sense do they converge? And this question is answered by the protagonist of this lecture, which is Birkoff-Fergody's theorem, but before that, just a notation, I've already defined this a n of f, and these are called Birkoff averages, and if I denote s n of f, by this I mean just the sum without taking, without dividing by n, so this is n minus one of f composed with Tk of x, and these are called Birkoff sums. I think Corina will use them, so I'm just fixing notation. So what is the result? Well, Stefan already briefly mentioned part of it during his lecture, so this is Birkoff-Fergody's theorem. Am I missing an idea? So what is the statement? Well, again, you fix a probability space, you fix a measure preserving transformation using the same notation as Lucia, so empty is a measure preserving transformation. Then for all f, the conclusion is that for all f in L1 of mu and for almost every x, this average converge, a n f of x, maybe I should say the limit, the limit of the Birkoff averages exists, and this is what Stefan already mentioned. So let me call this f bar of x where this limit exists. So the statement is also that the function f bar is actually a function in L1, so it's integrable and it's team variant. So this function is in L1, it's team variant and the integral of this function is the same as the integral of your starting function. The integral of f bar with respect to the mu is equal to the integral of f with respect to the mu. Is the statement clear? The average is converged for mu almost every x. So why is this theorem called ergodic theorem if there is no notion of ergodicity where there is an easy corollary, which might be the form you've seen before. With the assumption above, if T is also ergodic with respect to mu, then you can actually say what this limit is. Then for mu almost every x in x, you have that the limit of the Birkoff averages. And let me just rewrite it from zero to n minus one of f along the orbit. This is actually the integral of f with respect to the invariant ergodic measure. Let's prove this corollary, but it's actually an easy exercise. Well, you just apply the theorem that tells you that for mu almost every point, this limit exists. So f bar, which with the notation is this limit where it exists, is an invariant function by ergodicity. What happens by ergodicity? It's constant. F bar of x is equal to a constant mu almost everywhere. So now I just have to convince you that this constant is actually the integral of f. Well, but the integral of f with respect to the mu also by this statement of the theorem is the same as the integral of f bar. But f bar is a constant. So this integral is just constant times the measure of the space. And x is a probability space. So this is one. Is this clear? So I guess it was never stated explicitly, but what do we mean by mu almost every x? We mean that there exists a set with full measure on which this statement holds for every point. You want me to write it down or put it as a remark? Almost every means that there exists a set y such that the measure of y is one. So it has full measure such that for all y in y the conclusion holds. Whenever we say mu almost everywhere or almost surely we always mean that there exists a set of full measures where this happens or on the opposite. The set where this property faces zero measure. So here there is, this is a statement about measure preserving transformation, but all the examples we've seen, usually you add a topological space and you add a continuous map. And we've seen that for continuous map on topological spaces, compact topological spaces there always exist an invariant measure but maybe there are many of them. So let's think about what happens if we change. So this statement holds for every mu measure so Stefan already mentioned that but what happens if we take the same topological dynamical system but we consider different invariant measures? The limit exists maybe let's take two ergodic invariant measures so the term on the right changes, right? Because if you change the measure a priori the integral of f changes. So something on the left has to change as well. What changes on the left? What is the part on the left that depends on the measure? Actually there are two parts on the left that depend on the measure. The point x, so if this statement holds for this x for a measure maybe this x is not a good x for another ergodic measure and actually it's not, okay? But there's also another part that changes with the measure. It's not just the point. The transformation maybe you can take the same but the other thing that changes is the function. So remember that the assumption is that the function is in one of mu so it's integrable with respect to mu and if you change the measure the same function might be integrable for a measure but not integrable for another measure. So well I haven't put this in the exercise but maybe you can think a few minutes of taking a continuous dynamical system maybe one of the ones we already seen and take two ergodic measures and find a function which is in one of one but not in one of the other. So it's integrable with respect to one but not with respect to the other. So I'm not sure how to state this remark but be careful about which measures you are considering, okay? And the last remark is that I haven't stated but part of the theorem is also that the same convergence also in L1. The convergence, the statement is for mu almost everywhere so it's a point why it's almost everywhere convergence but the sequence of the Birkhoff average is converges also in the L1 norm. It's also the L1 norm which Lucia defined. I should speed up a little bit. So if the measure is not ergodic, this is not very precise what I'm about to say but if the measure is not ergodic the function you get here is a function which is, so ergodicity means that the system is in the composable from the measure theoretic point of view. So if the system is not ergodic it means that you can decompose it in different measure preserving system with positive measure. And you can think of, let me draw a picture but this is not precise so maybe your system can be split into several invariant pieces and what this function is is the average of this function but just on these separate pieces. So when you average, averages, you get the same average, right? Doesn't make sense what I'm saying. This is very vague but you would have to make this statement precise and you can but it would take more than an hour so. But anyway, you should think of this limit as the average on the minimal invariant subset of subsystem of your space. And then when you average of these averages you get the same average. But also you can think that, so the integral of F composed with T is the same as the integral of F because T is measure preserving. So the integral of A and of F is the same of the integral of F for every F. So the statement is just basically, this last part of the statement is I can exchange the integral and the limit which you can't always do but yeah. Some applications. So let's take a number in zero one and let's write it down in its decimal expansion. So x is not point x, zero x one, x one, two and so on. So this is the decimal expansion. So by this I mean that x can be written as an infinite sum of the xi divided by 10 to the i. Where xi is a digit between zero and nine. So one thing you might wonder is how many times the same digit occurs in the decimal expansion of a number? And what's the proportion of the digit two in the decimal expansion of a random number? And the statement is that if you count the number of times say one less than k, less than n, such that the digit i of x is some fixed digit l between zero and nine. So many times this happened divided by n. So what's the proportion that the digits, the digit else occurs in the decimal expansion of x is that for the bag almost every point, well this frequency tends one tenth. So each digit occurs with the frequency you expected to occur. So no digit is better than the other, basically. And so well the statement is that this limit exists and is equal to one tenth. How do we prove this? Well, if you take any number, for example, you first notice that x one, the first digit is equal to l. If and only if x belongs to the interval i l, which is l divided by 10, l plus one divided by 10. Okay, well first we have an issue because maybe the decimal expansion is not unique but we've already seen is Hannah's course when an expansion in base two or 10 is not unique. And this happens for countably many points. So when we look for a statement of almost every point, it's okay, we don't worry too much about what happens in zero measure set. So let's suppose that this expansion is unique, so you can meditate this in connection to Hannah's course. Well, this is kind of obvious. So consider the map e 10 of x, which is just a multiplication by 10, mod one. So we learn in primary school that when we multiply by 10, we just shift the dot to a different place, right? So then xk is equal to l if and only if e 10 of k minus one of x, the first digit of this number is equal to l. We've just shifted the k digit to the first place and the first digit is equal to l if and only if it belongs to i l. What is this number then? Well, the number of times up to n such that xk is equal to l, I can just sum for k from one to n of the characteristic function of the interval i l of e 10 to the k minus one. And for the sake of notation, let just me shift the indices. So here it was k minus one for k from one to n. So let me put from zero to n minus one and here we put k. Well, then we've seen, well, it was one of the exercises of Lucia's class. It was for the doubling map, but okay, you can do for exercise for the time 10 map, but this map is ergodic with respect to the Lebesgue measure. So we can apply the corollary of what Birkoff ergodic theorem in this form and this tells you that this average converge for mu almost every point, for Lebesgue almost every point, by Birkoff theorem, Birkoff ergodic theorem for this average converge to the integral of this function in the lambda inside a set of measure one. And let me call this set of measure one n then l, the measure of is equal to one. Okay, there exists a set of full measures such that the Birkoff averages converge to the integral of the function, but what is the integral of an indicator function is just a measure of the set. This is just a Lebesgue measure of il and il is this interval, so this is one over 10. So the set of points in zero one for which the digit l as an asymptotic frequency as measure one and this asymptotic frequency is 110. So the set of in zero one, which are normal and binormal, which are normal in base 10, and by normal in base 10, I mean that the frequency of the digit of any digit from zero to nine occurs with frequency one tenth, well, this set and then it's just the intersection of all this nl, just do the same thing for all the digits from zero to nine. All these sets have measure one, so this set has measure one as well. Is this set, which has measure one? Is this clear? I'll take it as a yes, if you have questions ask. Okay, maybe in three minutes, let's do another example. A function is T invariant, so okay, let me put it here. F is T invariant if mu almost every x in x is equal to f composed with T, so f of x is equal to f composed with T. So the value of the function is the same along all the orbit of T. So yeah, sorry, I didn't write too much. So this average, this average is have a limit by Birkoff-Ergodic theorem for Lebesgue almost every point. And this means that there exists a point with a set of measure one, such that this limit exists and is equal to one 10 for all the points in that set. And I'm just calling that set n. So by this n is an any letter, by this I mean, you write the number isn't based on and you look at the frequency of the digit L. Just because the set of all normal numbers is just the intersection of all these sets for L for all the digits from zero to nine. So we can compute the set of all the numbers with the same objects or the frequency at which some digit occurs, but maybe for the continued fraction expansion of a number. So the thought this is the continuous fraction expansion of x, and you ask yourself what is the frequency of zero from k and minus one of how many times does the digit L appear in the continuous fraction expansion of a number divided by n and you ask yourself does this limit exist and what is it? Well I'll go a bit faster if it's okay for everyone. And the key point is just to remember that a zero is equal to L if and only if x belongs to the set x belongs to the set what I have called it. P L is one over L plus one, one over L. So remember that the connection with the Gauss map, here we have one half, one third, one fourth and so on. One way of finding the continuous fraction expansion was you denote this interval P one, this interval P two and so on. And if a point lands here, well the first digit of the continuous fraction expansion is one and so on. So if it's here it's two, et cetera. And the Gauss map acts on the set on the continuous fraction expansion as a shift on the left. We all remember this. Okay, so well then a k is equal to L if and only if gk of x, well this is the Gauss map, belongs to P L. So you can conclude in the same way. I'm saying then, okay I haven't said this but you haven't seen this. We have seen that the Gauss map, that the back measure is invariant for the Gauss map and let me state it as a fact. The Gauss map is ergodic, not the back measure, sorry. With respect to the measure mu f, which is the measure of, which is density. So in Irena's notation, maybe I should have called it lambda f, in Irena's notation, when you do lambda f this means that this is the measure which has density f with respect to lambda. Where was the function one over log two times one over x plus one. I don't remember if she did it in class for an exercise but at least we checked that this, the Gauss map leaves this measuring variant and as a fact I'll tell you that it's also ergodic. And now you can just apply the theorem I'm raising by the ergodic theorem. Mu at lambda f, sorry. Lambda f, almost every x in zero one, the frequency divided by n, well this for almost every x, this converges as we did for the base two expansions to the integral of the characteristic function of pl with respect to this measure. But again the integral of the characteristic function is nothing but the measure of this interval. Okay, so maybe let me, so what is this measure? This is just pl. This measure is the Lebesgue measure with density one over ln two times one over x plus one. Lebesgue measure. This is the definition of this. And this is just the integral from one divided by l plus one to one over l of this function. If we remember from calculus, let's keep a few passages and I'll tell you that if you integrate these functions correctly you get one over ln two times ln of l plus one ln of l plus one squared divided by l times l plus two. If you wanna check, maybe I got it wrong. Okay, so the last 10 minutes I want to talk about unique ergodicity. Do you have any question on this part? So let's go back to the setting where xd is a compact metric space and t is a continuous map. So we've seen before with Stefano that theorem, this was really of both theorem, which Stefano told us about, that in this case there always exist mu, a Borel probability measure, which is team variant. But we've seen with Hannah that maybe, well, more often than not, there are way more than just one probability measure. So for example, if you have a periodic orbit, then every periodic orbit supports an invariant measure. And for example, in the case of E2, there are, or in the case of expanding maps of degree two, the set of periodic points is dense. So there are lots and lots of invariant measure. But now I want to consider the opposite case where there is just one invariant measure. So definition, we say that t is uniquely ergodic. There exists only one invariant probability measure. There exists only one team variant probability measure. And again, you might ask why is t called uniquely ergodic? If there is no ergodicity here, where there is a proposition or theorem, that tells you that if t is uniquely ergodic, then it's ergodic with respect to its only invariant probability measure. So if t is uniquely ergodic, then it's ergodic. It is ergodic with respect to its invariant. I'm not gonna prove this, but last time yesterday Lucia briefly mentioned that the set of all team variant probability measure is a convex set, and the extremal points are exactly the ergodic measure. So if your convex set is just a point, the extremal set is the point itself, and so it's ergodic. This is the idea, but I'm not gonna do the details. On the other hand, I'm proving another characterization, which should make a link with the first part of this class that says for a continuous to x, where x is compact metric space, the following are equivalent. It is uniquely ergodic for every, again, I mean the setting of topological spaces. So I can talk about continuous function. So for every continuous function, the Birkhoff averages converge to a constant c, depending only on the function and not on the point, constant for all x. The same thing where the convergence is uniform. Oh, that's it. Okay, maybe I should say. The convergence in part two is uniform across x. Okay, so this is a, well, you should think of vial theorem we've seen before. So for example, this theorem also tells you that in the case of rotations, since we've already proved two, well, the Lebesgue measure is the only invariant measure for the rotation. This was not obvious, I guess. Examples, by vial theorem, the rotation, an irrational rotation, where alpha is irrational, is uniquely ergodic. You will see in the exercises, and this I think is a bit challenging, but well, it would be, the statement would be precise in the exercise, but you should think of isometries are uniquely ergodic. We will see next week, probably, that interval exchange transformation that Corinna Briefer mentioned are typically, and this typically I think will be precise next week, uniquely ergodic. But on the other hand, expanding maps of the circle, x, expanding S1, the protagonists of Hannah's course, are not uniquely ergodic. And again, the reason is simply that, for example, as soon as you have periodic orbits, fixed points, well, each of those carry an invariant measure, so there are usually more than one. And this is always the case. For pastly chaotic systems, they will be more often, they will have plenty of invariant measures, or not just one, but for those which are sometimes called slowly chaotic systems. Typically, so with probability one, if you pick one at random, they will be uniquely ergodic. I guess I don't have much time for the proof. Maybe we can just prove one point in the last two minutes. Yeah, so just to have an idea of what techniques you could use to prove a statement like this, we can prove that one implies two. Well, you have to prove a statement for all points, so one thing you can look at is fix any point and just look at the sequence of measure supported on the orbit of, open some segment of the orbit of the point. So a from zero to n minus one of the Dirac delta at tk of x. Is it clear this? Yeah, we've seen this already with Stefano. You look at the sequence of points for all positive, for all the natural number n. Well, we've seen this is contained in the set of all probability measure on x, maybe it was called p, I don't know. And Stefano mentioned the set of probability measure is compact. So every time you have a sequence, there is a convergent subsequence. And well, the convergence and sequence we've seen this in Stefano's class again has to be an invariant, well, it wasn't in Stefano, it was one of the exercises from Stefano's class has to be an invariant measure for the transformation t. Any weak limit of this set is an invariant, but how many choices do you have for an invariant measure for a limit point? Just one. So can you have more than one limit point for this set? No, all the sequences to converge by unique ergodicity, by definition of unique ergodicity, all the limits point have to be the invariant measure. So all the sequence one over n of delta tk of x, all the sequence have to converge weekly star to the only invariant measure because you have no other choices. And by definition of weak star convergence, then all functions for all continuous function f, well, when you integrate f with respect to this measure here, this converges to the integral of f with respect to the measure mu. And what is this integral on the left? The Birkof average. So a and f of x converges to the integral. So I think I missed one line from the statement is, so this is the statement and if any of these solves, then this constant is the integral of f, sorry, the element. Then this constant is the integral of the function with respect to its own invariant measure. This proved that one implies two and that this constant, this is the cf. Any question?


Jurassic World Evolution 2 Battle Royale and today we are marking our fourth I think could even be third. I'm not too sure how we're doing this But whatever it is it is the next battle in the sequence Which will eventually lead up to a finale of likes of which have never been seen on that channel So last time if you watch the previous one, we had our winner, which was the blue Spinosaurus I don't know what the blue Spinosaurus is doing and what we said is after every winner you guys would get To nickname the dinosaur so today has been nicknamed by Spino Dragon Productions And they named after like the Japanese for blue devil, which apparently is Aoi ku. I know I was blue I'm guessing Aku Might be devil not too sure and that brings our finalists up to four It would have been five yet the blue devil killed our last one, so there's only four those arm sneak Cheerio, Aoi ku and now bamboo So what do we have installed this time? Well, this is the battle arena and it is filled with a plethora of new Dinosaurs every time we do a battle evolution royal thing whatever you want to call it We add new mods to the game now some of returning from previous ones And others are completely new so I'm very looking forward to seeing but what there's no Why do we not have a megalania? One of the newest mods coming to Jurassic World evolution to a hot-off nexus website is The friggin megalania and oh our looks so good look at this Look at that man. That looks awesome. I mean, I'm assuming it's it's like that metrodon They've done a few changes to it, but megalania is of course not the only thing that we have got added into this game But by Joe does it look glorious? Oh, look at you sat there. Aren't you cute? Yes, very good Okay, let's see what else we have in store of the new dinosaurs are this Mega Raptor which looks like something from Chaos Effect with that black to red contrast color look you've also got the Giga from the Warpath game for which was in the last one, but you know he's back again because why not we have the touch here Which is like an enkylosal now this is made by I think it's two guys And they have just like taken loads of models from you know dress a world alive And they put it into this game or at least you know it's like a teaser So I think we have Mortem Rex. We have Giganix. We have Inditoris But I mean we'll see them through of course. Why are you exactly the same? Are you kidding me? You are completely randomized and the Spinosaur we got it's not the same as it Salah del Huasco and Pultrana and the other one is chaplain vary and lithobytes.  That is so strange. All right, then. Well, we got another blue headed Spino in this one Oh here we go. We've got the hadrosaurus as well that we also have the columbia mammoth is back a very blue Kamara, so what was that from land before time? Of course the Tarbasaur from Camcretaceous is back. Oh God, I'm sorry just fly to the sky though. Don't know how well It's really gonna do here, but it's not the only Tarbasaur that exists in this battle arena We also have Giganix, which I think is the hybrid between Giganotosaurus and I think it's like Spino Rex or something like that I was like a three hybrid. Hey look for the Brachiosaurus. We got the Jurassic Park 3 one. Oh, that's brilliant There it is the Alberta Spino being another Jurassic World alive hybrid, but we actually have an official Utah Raptor and my God doesn't look gorgeous Completely feathered and everything love the colors on and look at those eyes We get a lovely front shot if it keeps its head. Oh, yeah, it's terrifying We also have this guy a silo sutus which I am as I'm assuming it's a carnival But it kind of looks similar to atheris in a source although very reptilian looking must be similar to Baryonyx or at least it looks like it is. This is another Tarbasaur. I don't know we've got this like Tarbasaur from Camcretaceous Tarbasaur and then there's Tarbasaur but ah Now let's see if we can find Bada. Oh, well, that wasn't hard was it? This one looks very similar to another Tarbasaur I don't know if it was like a walking with dinosaurs one But definitely from some sort of media with that coloring I've definitely seen that before it could even be the Tarbasaur from Planet Dinosaur that might be it There it is aoniraptor as well or aoniraptor I think this might be the one that's from Primeval? I could be wrong. I'm not too sure although it kind of gives that look with the white and dark ratio The white the white underbelly in the dark on the top another dinosaur in here to mix up the mini cup We will eventually see after a lot of the bigger dinosaurs are killed Oh, also, can we just take a look at this Seranosaurus like my god the coloring's on this guy It's amazing. I love it. Tethyshadros in again here with its beautiful markings Beautiful model, but I'm not expecting it to last long. Oh, well, what are you? Whoa? Oh, you're the other Megaraptor They am looking gorgeous. We could we had some like absolutely beautiful mods come out for this game And I'm very very interested to see who's gonna be the winner of this because not only do we have so many Amazing dinosaurs in Jurassic World Evolution 2 but with these mods. Oh God, it's gonna be gorgeous. Oh, yeah We got irritator irritators back as well. There it is We've got a lovely dark and brooding and Montosaurus. They won't look how is that? Whoa, Majugosaurus looking really cool with that skin one of those dinosaurs I'll I'll see like once in the battle and then it'll just be dead. It'll be killed by something. Oh, okay That's what happened to that. Oh Dolophosaurus being the bigger one with a bigger headcrest love to see it very similar to the previous Balwan what is going on and Indotaurus looking gorgeous walking on two legs the bipedal form We were promised from the concept of pop art of Indotaurus when eventually we got it It was walking on all fours like Indoraptor and it was like, oh Cool, but here it is in all of its glory By pedaling everything. Oh Yeah Micro serratus Making its final debut as a mod in Jurassic World Evolution 2 maybe someday we'll see it in an official DLC But for now at least we have you know a stand-in of sorts And there you go a T-Rex as well very similar to be Thomas Orbert off Markings, maybe it's trying to fit in here going under the radar.  Let's find out who will be our first casualty and for oh my Indotaur what Indotaurus in Dominus's start to hunt what oh? No, it's the Apatosaurus Cannotically correct Indotaur Indotaurus Indomitus Rex goes for a panosaurus. Oh here. We go. We got more fights Oh, oh an insta killed Dynonikus dies or Dynonikus dies to Rarosaurus We got Albertus Spino. Oh, we're what oh it hunt down this Stiggy I was gonna say is it gonna die already to what Mortar Rex taking on Chancisaurus and it looks like Mortar Rex might be winning that one Oh Thomasaurus, but are killed by the Giga and Kylosaurus against Alasaurus We don't know who's gonna win this looks like Albertus or sorry Alasaur is gonna win that one I am a to pot with the names apparently Scorpius Rex has just hunted down Model of the source and I was switching target to take down the Apatosaurus Working in tandem there with the Indomitus Rex Supermimus taking on a little bit of a challenge from the Nozuda seratops But I'm expecting a Zudas seratops not really a stand much of a chance and was that a Marga saw killed by Indomitus Rex Uns Completely standard there in Domino strikes killing the sauropods Albertus Spino going for the smaller ones killing an Archeonitha minus We've also got a Taurus or taking on it. Wait. What are you to run a Titan? Yeah, we didn't even see that guy to run a Titan. Who knows how that one's gonna go But I'm expecting to run a Titan to probably win that. Oh Dimetrodon taking on a Metricanthosaurus And they'll be really interesting to see how this one goes. Please tell me that it's gonna stand somewhat of a chance Don't take it down Spinosaurus taking on Albertus Spino. Oh, wow, this is gonna be interesting. I want to see this one Very rare we see.  Looks like spider might have won that one though Indo oh Indomitus Rex taking it down a Nijosaurus and this is Indoraptor is hunting the driest. Oh, bless it. It doesn't even know the deaths approaching but it survives Somehow I got bored or run out of stamina or something like that Men me there doesn't know the danger that it is. Oh god. We got Albertus Spino taking down the mammoth I think already it's it's trying to do something like that We got Sinus aerotops killed by Thovernade a fish eater and we won. Oh The Tarbasaur killed by Giga. That's Giga who's killed two of the Tarbasaur's Megalania here is still in the verdicts. I want that guy to win my my monies of Megalania I don't even know if I can have a fight against Indomitus Rex and even if it can Can it even kill it? Albertus Spino on 62% but taking down the Colombian mammoth there There is an aaurus didn't do too well last time I think it was one shot by something not too sure what it was, but I remember it being disappointing Oh, yeah, we've also got this guy. We've got the Drepenosaurus, which is a very odd creature Oh, is it acrocanthosaurus? Oh We got the Dynachyrus or Dynachyrus or Dynachyrus or something man. Has it killed it? Did it did it just kill acrocanthosaurus or was this just a fight? I have no idea Indomitus Rex now taking on Diplodocus where we're seeing what we see all the time with this guy and that is the slow extinction of Only giant sauropods because well apparently they're the ones that seem to go for it anything with Indomitus Rex in its name or in its blood Just seems to favor killing all of this.  Spinosaurus oh it was Scorpius Rex killed modern Rex Wow, okay Well, they have a horrorsaw taking on the Aliso not seeing this going very well for our source And well, they have it a beautiful coloring so I can't knock it for that But yeah, it's that much I can't be still going Look at it. Go gorgeous. Oh into Taurus doing something weird with there I don't even know what that is some sort of giant sauropod soratosaurus against Toronto Titan Is it gonna hold its own with 30 way how much 61%? It actually is will we see it finally in the final with Indominus Rex taking on Tarbas all from Camp Cretaceous, and he wrapped it just running around it.  I saw the markings go up on Tarbas, so but are they oh, oh, it's going back in and another dance All both looking kind of engine and Indominus Rex is the one to run away very interesting Oh, we have you to run is here as well. There's so many I haven't even seen this like Chelanthosaurus as well here I think Sukumimus against you to run us It would be amazing to see either of those near the end of the battle We've also got a baronix, and I think that is a name count it is chaos Wow That is quite interesting and all the combinations it could have been it chose to be a canonical soft cannon character from what you call it camp Cretaceous Not too sure what this guy's going for I think he's trying to take down the since data source, and there it goes Contorting it into the ground.  Oh, I'm so sorry He's not leaving you alone. There is it. Oh, hold on Megalania taking on a young gasaurus. Oh, I've got it. Oh chunking a source I've got to see this here. It's like the mini cup. Oh I didn't even know these two could fight. Oh, I think the Megalania killed it. Yes Brilliant. Oh look at it run Look at it a beautiful giant Lizard from prehistoric Australia and they are up to also there, but it's won its first battle. Yes. Come on It's like the world cup And I'm rooting for the underdog, but it's definitely not gonna win unless unless you never can tell Struthymimus has survived longer than freaking Morton Rex did. Anything is possible in this battle arena Being chancellors kind of has that werewolf look going on about it, but apparently oh no meet me Did it just get stepped on? One day Mimi will take down Indominus Rex, and it will be glorious One day not today Spinosaurus still thriving here chasing off the Tarbasaurus. Oh look at it. We've still got the giant Tino Kairis here. This is brilliant 100% health. Oh, we've got whoo whoo source against allosaurus and I well there goes that but also in the back We have oh, is it Megalosaurus against a Baroness and it looks like Baron X one Utah Raptor Has it made a kill? Probably not the moment. We've also got. Oh giganix again Saratosaurus and it's won it. Oh, you never can't tell a legendary Hybrid from Jurassic World alive. Will that make a difference? Does class mean anything in this game? Do I even know what I'm saying? No, not really. We've got a battle between car coward on the source and Dino Chiracy, I'm gonna say it different every time because I don't know how it's pronounced the giant crazy white eyes And did anybody win that? No, they just kind of all walked away from each other very interesting car Carnot or is killed by a crook and the source to dinosaurs I've barely seen any of and they are that all we got a T-Rex on 54% so it's definitely been in a battle with something in the towards against a younger soul And we could all guess how that one went. Yep. Indie Taurus definitely won that one pro Saratosaurus still surviving How else is it? Let's have a roll call. What else is dead? Oh Hunted down by the green Indoraptor a guanadon killed by Indoraptor as well. What a pose you get you look amazing there beautiful What else do we have here? We have the dead Alberta spino. Oh Alberta spider was killed by Spinosaurus. I was kind of interested to see how this one would go. Whoa Whoa mega raptor against ecthovenated to a modern dinosaurs fighting over the dead body of another Megoraptor can ecthovenated kill this one and even know how that one died, but they're calling it off So who killed this one? Baryonyx killed the Megoraptor. Wow. Oh Indoraptor taking down a modern Lachosaurus And is it right Saratops again? Chancisaurus and I think Chancisaurus is going to win this one. Will there be any herbivore in the end? I don't even think so. We don't even have stegas Saratops or anything here We've got a parasol being killed by Indoraptor. Yep Slowly the herbivores are now being hunted down Saratops managed to win or at least survive its battle and Kyla saw hitting the side of Sukumimus here I mean, I really feel like and Kyla saw would win this fight, but looks like Sukumimus actually won that one. Oh Is that a Montasaurus? Indoraptor killed a Montasaurus. Yeah. Yeah, we could definitely say that's what happened there a rematch between car car and on the source and the Dino Kairis Dino Kairis looks like it's in better shape but first it goes to the car car and on the source and Is that I mean you could never really tell Damn that's a tiny tail. Oh, no Taurus always killed. Oh, bless it Oh, we're teleporting around T-Rex is still surviving. I've barely seen any action from the T-Rex Oh, it's a victory to the Dino Kairis and This is Indominus Rex taking down the Alamosaurus. That's the one Baronex taking on the Megarafter now Baronex killed the last one and actually this Megarafter has just had a fight with Icthovenator Baryonix's own like cousin. Oh god knows what but it looks like Barry won that one Indotaurus is chasing down the Camarasaurus. Yeah. Oh There he goes using its psychic ability it crumbles the knees of the Camarasaurus Something's about to bite the dust and it begins with a TYT. Oh, no It's the beautiful modern creature. What's it called the Teth Shadros that one This is a fight between Indoraptor and Pyro Raptor. Oh, okay Well, I can't say I've ever seen a little Raptor managed to kill Indoraptor and yeah, just as I thought they're very much dead, but what's going on here? What did did you just win fight Victor? Wait? What did you kill? PNT. Oh, it killed the Zinoceratops. What are you doing? Friendly fire. Oh Indoraptor killing the myosaur. Thank god at least something's happening. Oh and Calisaur killed by Alasaurus No polar cat this I think has just been ended by Indominus. Wow It really feels like we've got so much more death happening this time 51 dinosaurs remaining out of like a hundred and nine I think it is we're about to see half of them gone extinct And the Taurus taking on a Megalosaurus now, and it looks like we've got a strobinator against Karkard anisaurus Is that something that can happen? It's happening and did it win? No, a strobinator is dead Now will Indotaurus even fight this thing? Oh Okay, okay. They actually do a fire. Oh, we got megalania irkins polar cat this is a sore palter God knows that's the one I'm more interested in. Oh the tail whip and all we killed it. Yes megalania is Kill something else. This has been fantastic for megalania fans and like myself It's been beautiful. Look people crowds of people cheering on megalania. Can you hear them? I can Yes But this fight wow, okay I didn't know how that went but Megalosaurus actually won that one and we've got Metricanthus Oh mutaburrasaurus being killed by Indoraptor Bloody cowards seem to be killing. Oh T-Rex against Dino Kairus kind of what Dino Kairus to win this one But I haven't seen T-Rex do many battles at all. So maybe it will win. Oh T-Rex actually bit it Do you know how many have you won? I'm very curious. You've lost two battles and won one. Oh, bless You know what? I love a triath. You love an underdog story And we have a fight between Therizinosaurus and Giga a rematch from Dominion and who's gonna win this one? Oh, they're slashing claws from the Thera although Therizinosaurus. Oh, yeah has been hurt and the Giga Does win that one. I love it. Oh some about its head but elongation. It's a bit creepy But I kind of like it who is killing the patchy cephalosaurus.  Maybe it's clever Maybe they deliberately building up their experience working towards the bigger prey. Who knows? Oh Ceratosaurus was killed by Indutaurus. Oh, that's a shame. Oh, we have the dead Yutaranus here dead Karnataurus Alasaur against Super Mimus this matchup It's normally the Alasaur that wins it. I don't know maybe it starts just generally better and Alasaur does go For the first by damn Last I was hoping it'd be super Mimus, but no I feel like if anyone's gonna win this one It will be Alasaurus Yeah, it looks like super Mimus Yeah, a lot of scars showing up on there and Spinosaur comes with a smack down on the Alasaur man! If only. If only you can have battles like that It's a bit of a shame that you have this here attacks that then that attacks that You can't just have some carnage where a triceratops runs through and just like impales something Absolutely love that. I love this old thing as well though. Oh T-Rex against Pentaceratops It's saying that man. We have a triceraptor against the freaking megalania. I need to see it Oh, it actually goes for the first time. Yes, does it kill it right away? Oh, and then it hit from the a triceraptor. Oh, no, no, it's cut as a fading Oh, how's T-Rex doing? Is T-Rex dead? Where's T-Rex? Oh, T-Rex is running. Okay, T-Rex lost to the Pentaceratops But this is the battle we really care about come on megalania. You've got this you went first. You did the first hit I think Who won? Is anyone gonna win? No, no, no megalania! You have the venom or something.  Poison health loss for five minutes. It's all about the strategy I like it another dinosaur that barely sees any action stuff I'd last it for all of two seconds Hmm is the compsagnathus still alive? I don't see any of the tiny little critters though I don't see the microseratis. I don't see listrosaurus. I think they might have just been gobbled up if I'm gonna be able to Oh wait, hold on. Yes, microseratis still lives But as long as a velociraptor or something with that kind of animation still exists They are not safe and scobies are against acrocanthosaurus and gets the poison Oh, no, it's not looking good and 43 percent. That's a solid hit and another hitting down to 20 percent A battle that really doesn't need to happen here a therosinosaurus against the torch here Oh the slash Some experience for the therosinosaurus. It takes the scars with it and the experience from that battle My god, it is absolutely ginormous in comparison to gigaspinosaur Indominus rex taking on the silechuchus or silechuchus or something like that this this weird thing Which I can't tell is a herbivore or a carnivore, but does get a fight back Two little scars and then get scared away and there it is. There's my boy. Yes, you could do this I believe in you The spotless record indoor raptor against a carcoranthosaurus There's still bearing scars of previous losses Anything you have any scars.   Oh torus is not dead. Okay. We'll see how that one goes We can get two battles in here once Oh, shut down from the carcoranthosaurus. I don't know what these two are doing. Oh, okay.  It's looking a bit worse for where and a hit from the torus so as well Looks like indoor raptor might have won this unless they're gonna finish it up here. Uh, oh, no, okay another hit. I'll take that and a whoo It looks like actually maybe the This one definitely went in the favor of the indoor raptor that one. They both kind. Oh, I love that It must be like is it the indominus rex animation to put its hands down on that looks so cool though Torusor held its own better than the other one did and oh We are seeing the final moments of sucomymus's life flash before its eyes before its life gets swiftly ended By an allosaurus's more and there it is Oh Left its neck too open and the crunch down an instant death Oh, we have the baronix against dino kairis. Can it redeem itself? It's like five times the the size of baronix, but no baronix gets the first hit It does get a rebound though. We also have scorpious rex against stegosaurus now And you know, you never know. No, okay. Looks like it's probably gonna die there. Oh, no, did the kairis Oh Barionix you you are looking so clean and actually wins. That's three losses for the kairis Plus it does try its best and scorpious rex against stegosaurus Stegosaurus on 34 percent and bleeding for the next five minutes My boy megalania against a uter raptor. Come on. You got this. No Oh Is it life? I think yep. Yep. It's okay. It's a megalania. You got it. Yeah, that's right. Knock it down Knock down the six foot turkey. You got this A battle in the water megalania in its element. It's a lizard. It's a slithery boy Come on. No, it's not looking too good though Get one more hitting buddy.  That's two losses for megalania and it just splashes away Uteraptor wins that one. It's like camcretaceous in that weird little spin-off episode Tarbasaur haven't seen it in ages and rexie as well. Oh Don't know what's going on here. Both both not looking too good. Oh, Tarbasaur loses Could this be a comeback for rexie and torosaur against in the torus both not looking too good Ah and torusaur loses Okay, that's fine a win for the regular and then a win for the mod. I'll take it.  Oh into torus Indominus rex has been absolutely ripped apart by something. Good god. Oh velociraptor against indoraptor Yep, and that's uh, that's an inch of death for the velociraptor I think a raptor can kill an indominus rex there is an animation for it But if it's on 100 it's gonna win. Oh my oh, what have we ended with two spider souls, man The showdown between the two last raptors atrosaur raptor and utor raptor a feathered paleo accurate raptor against a an abomination of well, hollywood And oh that mod so it's hard to tell how this one's gonna go unless you just randomly drop Okay, it was a fight. It was a regular fight a few scars in the utor raptor. That's okay. That's good. That's good Still working it out. Still. Oh, oh the hit down. Oh, it didn't get grabbed by the neck. That's good It looks like it's gonna be a Oh, no some scars appearing on the atrosaur raptor there if it's a bit janky. Oh the paleness from the atrosaur raptor now Yeah, utor raptor won that one get in Feathers been scalish Ender raptor has not lost a single battle. This will be interesting 27 dinosaurs remain Wait, what happened to the aoniraptor and the mega raptor? Where did those guys go? Oh, acrocanthosaurus killed by the spinosaurus there. I must have missed that one Scorpius rex killed the silicaeaurus irritated killed by scorpius rex. Okay. Scorpius rex is getting a lot of kills in here No, megalania, you bugger you Ender torus killed it. No He was saying that he probably didn't even stand a chance two wins one loss. Oh Forever, we will remember you very sad, but if you close you Oh, is this a spinosaur versus an indoor raptor you got there is anosaurus just walking along the swamp Oh, hey, I say that. Oh gigaspinosaur. Yeah.  Oh just instantly killing car carad anosaurus. It's the eyebrows menacing looking An old favorite allosaurus taking on indoor raptor now indoor raptor I think maybe is being in one battle But even then it was barely a fight and oh the hit straight from indoor raptor You know what? We see indoor raptor gets so close to the end the same with indominus rex But yet we have not had it win yet. Can this be it's time to shine Allosaurus not even getting a single hidden has bloody Red eyes and is it going to be at least one hit? Oh, okay. Okay one hit Can I get another one in I feel like something's happening behind me? I don't know what oh, it's scoping strikes against dine and carries here it is again Is it going to get its fifth loss or god knows what?  Just gonna just gonna take the poison and run away cool Oh the poison from megalania is still taking effect on uteraptor and it worked against the uh The uh triceraptor. So that's really interesting triceratops are still alive. Didn't I lose one? And torus fresh off its victory against a torus or is now trying to take on pentaseratops and um I don't know. I think that was a that was a bad idea Going for the uh the moose version and Not only is it taking a full-on What do you call it? I don't know thrust from the horns, but it got denied and I don't even think it took any damage Damn pentaseratops really uh showing it stuff there against indetorus. How are you still alive? How many losses do you have? No, you have more than three. I'm sorry. You have way and that's more than one scar Oh chan just saw I haven't seen oh copy is still alive Yes, wait. It was down there somewhere. Okay. I don't know.  Oh, I I have I have no idea what happened there Oh the giga and the therizonosaurus resuming their battle I don't even know who won it last time. I think it was the giga won it Um also the giga went for the first hit, which I think Yep, it's not gonna be an outright victory. There's a lot of close battles in this one. I'll have so just Uh, okay, I'll go you all right buddy like learning. I must watch Learn my foes attacks and then maybe I can win giga another win for it That's a lot of victories for this guy Six victories. Oh never mind.  I don't think there's an outright like guaranteed victor here Oh, no rex. He died to scorpious rex. What happened there? Okay, alas Oh my god, choice. No Oh my god, choice. Oh I'm making a comeback Finishing up alison one hit. That was amazing You never can't tell how these are gonna. And dino kairos finally meets its end to the indoor raptor. Oh, okay Off it bounces jiggling its way to victory scorpious rex. I feel like has a lot of kills Nine victories That might be the most amount of victories we've had in a single combatant Oh into torus trying to like win this little victory against it already beat up therizonosaurus I kind of want therizonosaurus, but no, just go on give it a slash go on kill it kill it and more Into torus has had some time to uh heal I was so hoping I was so hoping it would just be like no shut up That's not fair, but then again, this is the name of the game take advantage of everything that you can and uh another I think they are both like out of energy And although it is a win for indoor torus. Oh, I love the saliva there I don't think it's a win-win for indoor torus if you know what I mean But I don't think it was a single winner there scorpious rex against barry Okay, I think barry onyx did go for the initial hit and another but oh No, the puffer face that is scorpious rex showing its scars. It's got one hit against barry Can he get another one to secure?  You don't have to do so good though. It seems so cheap Damn indoor raptor. Well barryx won that one, but now he's going to be losing health for the next five minutes Though it looked like it definitely did more damage And unfortunately, I just managed to catch that there our feathered beauty The uter raptor fell victim to the indoor raptor doesn't seem fair really But we do have two seratopsids in the final triceratops and pentaceratops I don't know we we've had one herbivore make it through to the finale so far and that was stegosaurus And we all know what an upset that one was So could we be seeing penta seratops and triceratops make it in there as well? Spinosaur and albedosaurus now going at it on the carcass Of the acrocanthosaurus or carcara dinosaurus that the albedosaurus kill and albedosaurus gets the first hit of what? What is this? Nonsense, I tell you one bite and that was enough for spinosaur to skedaddle out of there. Wow Well, I mentioned about a seratopsid making it into the finale and pentaceratops is now taking on indoor raptor I don't know how this one's gonna go and Actually it would be so cool if it just got impaled as I turned to it and it just went on the horns A bit like it would have died in falling kingdom But it does get off the first hit can pentaceratops at least get a hit off it can do okay So it's holding its own interrupter has no venom has no bleed So it's gonna have to kill pentaceratops through a brute strength and gets a second hit off pentaceratops Yeah, that's done a lot of damage interrupter not showing too much But pentaceratops might get another hit off and there it goes another hit is inter interrupter going to be losing and It's about a medium Yeah pentaceratops looking the worst one here scorpious rex and baronix resuming their battle I think baronix got the uh the first hit off there scorpious rex not looking good This could be the final uh fight for scorpious rex. I'm thinking if baronix can just finish it Uh scorpious scorpious rex really relying on the venom to do the hard work and it's gonna get away with it again Changesaurus against albertasaurus I don't know albertasaurus secured a lot of victories recently and again gets the first hit off It's the mini t rex and it is doing it. It's it's going getting the first bite off But it's just I mean wait what How can we just bite once and then they all cower in fear against I have no idea what the hell's going on here Oh, we have spinosaurus against scorpious rex They didn't bite off more than it could chew and it did. Oh spinosaurus puts an end To scorpious rex's venom reign baronix can now Breathe a sight of relief knowing that its rival has now Been defeated and I think the poison is just about oh wait what it's went back up. I'm pretty sure it was on a minute before Oh, maybe that's a revenge venom effect But scorpious rex is out of there. It had so many victories as well nine victories and then two losses And baronix still feeling the effect of the venom is facing off against Changesaurus I think we know how this one's gonna go And baronix unfortunately collapses to the floor changesaurus taking a victory And a triceraptor unfortunately is gonna meet its end at the hands or paws and claws Of indoraptor meaning that if copy is still alive It survived You did it Unless you've been in a battle. Have you okay? If if any dinosaur survives to the end of the battle and it has won a battle Then I will put it through to the finale This way we stop anything that's just been running around and hasn't killed anything Getting through to finale, which doesn't really feel fair There is anisaurus with three wins and three losses and two kills actually and the feud Continues between a giga and there is anisaurus And the giga gets the first bite off again They took a long hiatus both of four other things and now the grudge match continues between these two Tell us all this time Claws as long as twine. I don't know Look at that face and again just as always Giga beats there is anisaurus but has still not put an end to its reign Wait, I didn't even see this not only is indoraptor killed pentaseratops But now it's facing off against triceratops. Oh, no Now I know triceratops has killed something that much we can establish and Oh, no, it's not looking good. I mean it's an indoraptor What do we expect here? When did indotaurus die? Did I miss that tlc?  Oh, okay Okay, okay. Ah, and we have a proseratosaurus against indoraptor I wonder who's gonna win And finally after 15th million time canned giga put an end to therizinosaurus and it does there we go finally puts it out of its misery You know what they're tenacious these long fingered Creatures dinochiris therizinosaurus they do well And then you've just got like a little compi just hiding in the grass here All right triceratops has decided to change up its opponent. It's no longer taking on indoraptor Probably goes indoraptors killing probably that other one cilia feisers, but it's taking on chancisaurus Chancisaurus being a bit of a dark horse here goes for the first hit Uh has done a lot of damage. This could be it Although I said that every time and then triceratops always does get a hit off Okay, look like it kind of dodged out the way rather than got hit So Oh, okay. Okay, a little bit of a scuffle on both sides Uh chancisaurus really not taking any damage from that whatsoever Triceratops taking the brunt of it however, and here we go two juggernauts now spinosaur Against albertasaurus albert against spino And who's gonna go first? Oh, it's a spinosaur taking on a huge amount of damage straight away I don't know this could be it. I feel like maybe it's down to Albertasaurus and indoraptor. I don't think those two Um paths have crossed yet and uh, oh Damn that damage from albertasaurus. Look at that That is impressive for a dinosaur that I don't know. It's it's like a you know, it's a medium. It's not too big It's not too small Kind of like an underdog. I would say and giga against chancisaurus Let's see how this one goes and the giga goes first. Oh Okay, so far my favorites giga indo and What was it albert? I think those those three are going to be the finalists. I get the feeling Uh chancisaurus. I mean if chancisaurus not doing too hot against this guy I can only imagine the power of it and look who decides to sliver to the plate Friggin slimy indoraptor Taking on spinosaurus and taking the kill away From albertasaurus completely bent. It's back in there and oh Oh Now it depends how this game works. I don't know whether like victories are worth more than um like kills or god knows what but Green oh Evil evil I mean it's tactical at the end of the day It waited until it was really weak and then it went for it. So I don't know it's it's supposed to be intelligent and there it is showing its intelligence And can the giga put the stopper in a chancisaurus life? I probably think so. Oh, but it didn't do it right away Really? You're not you're not going to do it right away. Go for another one Just one more bite. I think you can probably do it one more bite Okay, you're gonna take a hit first. All right.  Oh god. Look at it. No It's so dead Just one more just go for it. Just one. Oh the cold.  Jesus Oh, okay. Yeah, didn't even get a single head in And the giga wins that one. Damn. Okay Maybe that might push the giga to the top now With all of that experience that it just got from killing indoraptor taking it's what what do you want if it's be level three? That's it undisputed nine victories and four kills Oh a changer saw finally it has been I think 20 minutes of fights going backwards and forwards, but we finally have a kill changer saw takes down the final Herb of all in the arena leaving a changer saw a giga And albertasaurus. Oh, this might be it an injured changer source against the giga Oh If they decided to keep on fighting possibly, please it's been it. Oh, there it is Changers saw dies. You have no idea. It's been like half an hour They've been like one bite walk away one bite walk away. In fact every battle has been one bite walk away and finally The giga Sets right the world and is almost instantly challenging the albertasaurus after its victory of killing changer saw is taking its victories now to 15 changer saw was on six losses Everything has lost to giga about five times now.  It's done against it and now its infamy level is two Oh, no. Oh, this could be it Thank god another 50 minutes later After a second battle, will they actually finish it? I'm not going to touch anything because I don't want to risk it. Yes Finally the giga kills the albertasaurus. It was getting to a point guys when I was like Should I should I just like Declare the gig of the winner and just be like, you know what there it is It was gonna happen. It was gonna eventually kill him and finally 18 victories and we have our winner That is the most amount of victories any of our winners has has attained. I think the spinus So only has 10 victories the stego has eight victories And then even was aggerio has 12 The giga has been fighting this battle for so long. It fought the changisaur It fought the albertasaur I'm kind of glad actually changisaur didn't win because we've already got one But finally giga has been a new victor. It's been achieved. Yeah. Thank you Oh my god, and finally now you guys can put in the comments what you want to call The victor try not to say what dinosaur it is because You know if people are just coming to the video, they'll see the comment and go. Oh, so that's who wins. Okay So try and be a little bit secretive about it We'll move it into the enclosure and until next time Maybe we'll do one or two more and then I want to take all the finalists into like a challenge sort of arena Maybe we'll do some races. Maybe there'll be like whoever eats the goat wins points I want to do something more than just you know a battle royale in the end Maybe we can do a battle royale and see who actually wins. Maybe we'll have a winner But then another dinosaur won because it had more points. I don't know Leave a comment. Leave a comment down below if you've got an idea until next time guys If you enjoyed the video leave a like until next time. I'll see you cuties later. Bye. Bye


All right, so here's your how-to on orbital notation. To start orbital notation, the first thing you need is an electron configuration. To do an electron configuration, you need to have your orbitals in order from lowest energy to highest energy.  Level number 2 grows a little bit and has both s and p orbitals. So we have 2s and 2p. Level number 3 grows further still and has sps and d's. And 3s and 3p would be the next two orbitals in order. But we have to follow the off-bob principle in dealing with the d orbital. It says the d orbital can't be filled until the s orbital on the next level has. So we can't just jump to 3d. We have to do 4s and then come back to 3d. At which point that we can pick up where we left off, we have 4s, so the next one up is 4p. And the next one would be 4d. But again, the rule is we can't put anything in 4d until we've done 5s. Now according to the standards and what I understand, we can't go beyond atomic number 38, which is strontium. And that's where we did right there. 4 5s would be the last orbital in strontium atom. So there's really no need to go any further. So let's do a quick electron configuration. Let's do the electron configuration for a nice big one this time. Let's do it for selenium. Selenium is atomic number 34. That means it has 34 electrons for us to put in the electron configuration. So we just start at the beginning and work away across until we put 34 electrons away. So the 1s orbital can hold two electrons. All s orbitals can hold two electrons and no more. Next one up is 2s. It holds two electrons as well. Next one up is 2p. p orbitals can hold 6. And again, if you forget that, spdf. That's the order of orbitals. Just write down your odd numbers, 1, 3, 5, and 7. That's the number of suborbitals they have. And because your number of electrons multiply that by 2. So 2 in the s, 3 times 2, 6 in the p, 5 times 2, 10 in the d, 7 times 2, 14 in the f. So you ever forget your limits, just do that. 1, 3, 5, 7, 2, 6, 10, 14. Just double it all up. Back to what we're doing. 2 plus 2 is 4 plus 6 is 10. We have 10 of our 34. We still got 24 to go, so we've got a ways to go yet. Next one up is 3s. And again, an s holds 2. Next one up is 3p. A p holds 6. And then the next one up is 4s. It holds 2. Good time to see where we're at. See how close to that 34 we're getting. 2 plus 2 is 4. Plus 6 is 10. Plus 2 is 12. Plus 6 is 18. Plus 2 is 20. So we still have 14 more to go. So 3d is next. And d's hold 10. So that's 10 of our 14. We only have 4 left. 4p's the next orbital. And we can stick them all right in there. So that's the electron configuration for selenium. And the first level, we have an s orbital with 2. And the second level, we have an s orbital with p. And the second energy level, a p orbital with 6. Third energy level, s with 2. Third energy level, a p with 6. And the third energy level, a d with 10. Level number 4 has an s with 2. And a p with 4. As far as valence electrons are concerned, we have 4s2 and 4p6. That's my outermost energy level. 2 and 4 is 6, which makes sense because selenium isn't group 16. So there's a lot of ways to check yourself to make sure you've done these right. Add those all up and make sure they equal the number of electrons you're supposed to have. Check that valence electron thing to see if you've got the right number of valence electrons. There's a lot of ways to look at it to see if you've done it right. Now on to orbital notation. In orbital notation, we just want to draw this. We want to show what it looks like. Put little arrows in to represent the electrons. Show all the suborbital stuff like that. That's based on this right here.  That blank represents your sublevel. And then you're going to put arrows on that blank that represent the electrons. One arrow going up, the other one going down to show that opposite spin that the poly exclusion principle says we have to have. S orbitals have one sublevel. So when you get to an S orbital, all you got to do is draw a little line and label it what orbital it is, 1s. This S orbital has two electrons in it. So an arrow going up and an arrow going down. Again, opposite spin. Next orbital is 2s. And again, the S orbital has one sublevel. So it's 2s. Again, two electrons. So one going up, the other going down. Now we've got a p orbital. There are three subopitals, three compartments, three rooms in the p orbitals. That's how we get that total of 6. There's three sublevels. So we draw in our three little lines, bracket it, and call it 2p, and get ready to put our electrons in. Now as a general rule, whenever you're doing p or d orbitals, whenever you have multiple sublevels, it's one electron in each suborbital first. And then you can go back and double them up. What that does is it means when we get to the end, if we have a partially filled orbital, we're going to have the minimum number of pairs, which is what it's all about. We want to minimize repulsion. That means the minimum number of pairs. So we do one in each sublevel. And then we come back and double them up. It's not going to be as big a deal here on the inside. Then when we get it to the end here, it's going to be really important. So that's 2p. Next one up is 3s. So again, s is just a single line. It's got 2 in it. Now another p orbital. 1, 2, 3 sublevels, call them 3p. Again, it's 6. One on each level, then double them up. 1, 2, 3, 4, 5, and 6. And again, this is just like stoichiometry.  Start trying a shortcut, and that's when you're going to make mistakes. So after 3p is 4s, 4s is a single orbital. So just a single line, 2 electrons in it, 1 up, 1 down. And then the next one is d. 5 sublevels and a d orbital. So you've got it 5 lines. And call them 3d. And again, there's 10 in there, 1 on each line, then double them up. 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. Now we've reached the end. p orbital, 3 sublevels on 4p. Here's where it's really important. 1 per level, then double them up, because we're only going to put 4 in this time. And there's a way 4 has to look. Has to look like this. 1, 2, 3, 4, 1 double and 2 singles. That minimizes the number of doubles, which minimizes the repulsion, which means lowest energy state. And everything in the universe wants to be in its lowest energy state. So that is the orbital diagram for selenium. Granted, that's a huge one. But that is about as complicated as you get. There's really only four more elements beyond that that we would do. So that's about as tough as it come. Let's do a smaller one, just for the sake of doing a smaller one. Let's do phosphorus. Phosphorus is atomic number 15, so it has 15 electrons. So what we've got to do is do the electron configuration first. So back up to this, first orbital is a 1s. It can hold 2. 2 of the 15 down, 13 to go. Next orbital is 2s. As is hold 2, 4 down, 11 to go. Next orbital is 2p. P's can hold 6. 2 plus 2 is 4, plus 6 is 10. We still have 5 to go. Next orbital is 3s. We can stick 2 there. Now we're up to 12. We have three more to go, and all three fit in the 3p orbital. Again, total them up. 2 plus 2 is 4, plus 6 is 10, plus 2 is 12, plus 3 is 15. We've got the right number of electrons in there. You can check your valence electrons to make sure you did it right. Level 3 is our top most level. 2 plus 3 is 5. Phosphorus is in group 15. It's supposed to have 5. Three energy levels. I mean, there's a lot of ways to make sure that we're on the right track with this. Now it's time to draw it. We start with the 1s. That is a single blank. Label it 1s. Two electrons in it. One up, one down. Again, one blank because it is a single orbital. 2s. Single line again. Two electrons. One up, one down. Remember, the p is this collection of three sub orbitals. So three blanks. Fill it up one at a time until you get to 6. 1, 2, 3. Those are ups. Now we'll start doubling up the down arrows. 4, 5, 6. Next up is an s. Two electrons. One up and down. And finally the 3p. Three electrons. Again, one at a time and then you can double them up. That's it. All three are in there. All three are up. There's no downs to do this one. All singles, no repulsion. That's the way it needs to be. Minimum number of doubles.