Combinatorics and Higher Dimensions - Numberphile
Featuring Federico Ardila from San Francisco State University - filmed at MSRI. More links & stuff in full description below ↓↓↓ Federico previously on ...
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Combinatorics is the study of possibilities. So, you know, if you have a given set, how many subsets might it have? Or if we have a given set, how can you arrange it in a line? So I want to talk about these questions but I want to talk about them from a geometric point of view. Let's do an example. So let's say, we have a set of 3 elements A, B, and C. Now, I want to figure out, what are the possible subsets? Usually the notation that we use is {} -> this one. But just to make it a little bit easier to read, I am just going to add it like this -> abc And so, a subset is just choosing some of these, and... and not others. And so, I might chose for example: A, B, or C. Or I might chose A and B. Or I might chose B and C. Or I might chose A and C. I could choose all of the...
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Combinatorics is the study of possibilities. So, you know, if you have a given set, how many subsets might it have? Or if we have a given set, how can you arrange it in a line? So I want to talk about these questions but I want to talk about them from a geometric point of view. Let's do an example. So let's say, we have a set of 3 elements A, B, and C. Now, I want to figure out, what are the possible subsets? Usually the notation that we use is {} -> this one. But just to make it a little bit easier to read, I am just going to add it like this -> abc And so, a subset is just choosing some of these, and... and not others. And so, I might chose for example: A, B, or C. Or I might chose A and B. Or I might chose B and C. Or I might chose A and C. I could choose all of the...
