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Mathematics

Cantor's Diagonal Argument and Uncountability of the Real Numbers

Quick fact

Cantor's diagonal argument proves that the real numbers are uncountable, meaning no matter how you try to list all real numbers, there will always be one you missed. This was the first time mathematicians had a rigorous proof that some infinities are larger than others.

Why this is interesting

You know there are infinitely many numbers—but are all infinities the same size? What if one infinity could be so large that it couldn't be listed even with infinite time?

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Cantor's Diagonal Argument and Uncountability of the Real Numbers

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