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The Nature of Infinity: An Introduction to Georg Cantor's Ideas
- nyc111 8y agoMinor typo I think: Proof of the Countability of the Rational numbers ℚ Let us first propose that the set of rational numbers ℚ is countable. To prove this assertion, let us arrange all the rational numbers (ratios of natural numbers) in an infinite table as such: 1/1 1/2 1/3 1/4 1/5 ... 2/1 2/2 2/3 2/4 2/5 ... 3/1 3/2 3/3 3/4 3/5 ... 4/1 4/2 4/3 4/4 4/5 ... 5/1 5/2 5/3 5/4 6/5 ... ... ... ... ... ... The last fraction should be 5/5, no? Not 6/5.
- jorgenveisdal 8y agoThanks! Quite right