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Science

Lionel Mandrake

(4,201 posts)

4. Cantor's diagonal argument shows there are more real numbers than integers.

Reply to erronis (Original post)

Tue Feb 24, 2026, 01:44 AM

17 hrs ago

Suppose the contrary. Then there exists a sequence containing the decimal expansions of all real numbers between 0 and 1. Let x be a decimal expansion whose kth digit differs from that of the kth number in the sequence. Then x is not in the sequence, a contradiction.

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erronis

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Highlight:

How Can Infinity Come in Many Sizes? -- Quanta Magazine [View all] erronis Yesterday OP

Fascinating! Doodley Yesterday #1

I studied this stuff when I was a math major 50+ years ago hvn_nbr_2 Yesterday #2

I've been enjoying Quanta Magazine's articles for several years erronis Yesterday #3

Quanta and my handle hvn_nbr_2 8 hrs ago #6

Fascinating. I have never thought to equate the various teachings in the bible to the "three-age system" erronis 7 hrs ago #7

Cantor's diagonal argument shows there are more real numbers than integers. Lionel Mandrake 17 hrs ago #4

I was just reading that a while back jfz9580m 9 hrs ago #5