More Sheep than You Can Count: Transfinite Cardinal Numbers


What are we talking about today. We're talking about cardinal. Infinity is obviously yes now. You you said infinity's the i love the title. If i may real quick the title of the show is more sheep than you can count obviously. That's an allusion to infinity. I love it a fantastic and the reason why we chose that is because there are sets of things collections of things that cannot be counted and And i mean there's a very real sense like not even all the real numbers right like not real numbers. All natural numbers right one two three four five et cetera. You can count all of them. Theoretically they are called countable because you can put them all in a list that has the first item at the first place the second item at the second place on and on and cover all of them. There are some sets. You cannot do that. With and one of those sets is the set of real numbers. And we'll show why on here but basically you cannot. You cannot list all the real numbers in any way shape or form. You will always leave things out any list no matter if it's infinitely long the really nuanced facts about infinity and that will we've we've realized in the field of mathematics and the last two hundred years one thing. I love about this episode. Though is i got especially interested in this topic when i taught sixth grade math. And what's cool is we're going to get into this in a little while but we had to do these socratic seminars. At the school. I taught out it was a charter. School and the kids started exploring infinity completely on their own and they had these group discussions that got into this and what i found a wonderful is there are. There's absolute overlap between some of their discussions. Like i think one of the topics that was brought up was does a circle. Have the same amount of points as a sphere and yes. I kid you not that we had sixth-graders talking about this socratic discussion. Not not everything was maybe correct in that discussion but most touches on the kind of cardinal anthony that we're gonna talk about today for example the answer to the question of does a circle have the same amount of points. A sphere surprisingly is yes and we will find out why.

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