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billwadge.com | ||
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ianwrightsite.wordpress.com
Are Cantor's higher infinities really real? |
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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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blog.vinneycavallo.com
An introduction to countably and uncountably infinite sets and cantor's diagonal argument |
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wildtopology.com
Let $latex D_n\subseteq\mathbb{R}^2$ be the disk of radius $latex 1/n$ centered at $latex (1/n,0)$ with basepoint $latex b_0=(0,0)$. Let $latex C_n=\partial D_n$ so that $latex \mathbb{E}=\bigcup_{n\in\mathbb{N}}C_{n}$ is the usual infinite earring. Let $latex E_n$ be a closed disk contained in the open set $latex D_n\backslash D_{n+1}$. Embed $latex D$ in the xy-plane of $latex \mathbb{R}^3$.... |
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