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kpknudson.com | ||
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ianwrightsite.wordpress.com
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| | | | | Are Cantor's higher infinities really real? | |
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mathbabe.org
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| | | | | 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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www.jeremykun.com
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| | | | | 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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rapuran.wordpress.com
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| | | [AI summary] A blog post discussing a weekly photo challenge featuring a descent-themed image, with reader comments and archive links. | ||
