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kpknudson.com | ||
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afnan.io
What is Infinity? We are going to start this post by trying to figure out what infinity is. What do you think of when you think of infinity? Most people know that it's this uncountable number or thing (or is it...?). There is no beginning or end, it just goes on forever. |
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www.jeremykun.com
Problem: Show there are finitely many primes. "Solution": Suppose to the contrary there are infinitely many primes. Let $ P$ be the set of primes, and $ S$ the set of square-free natural numbers (numbers whose prime factorization has no repeated factors). To each square-free number $ n \in S$ there corresponds a subset of primes, specifically the primes which make up $ n$'s prime factorization. Similarly, any subset $ Q \subset P$ of primes corresponds to a number in $ S$, since we can simply multiply all numbers in $ Q$ together to get a square-free number. |
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mathbabe.org
A continuation ofthis, where I take notes on my workshop atHCSSiM. The real numbers are uncountable Today we used Cantor's diagonal argument to prove that the real numbers aren't countable. Namely, we assumed they were, and that we had a bijection $latex f: \mathbb{N} \rightarrow \mathbb{R}$ and then proved it didn't contain the real number... |
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thewayofthefly.wordpress.com
Visit the post for more. |
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