The Axiom of Infinity

Re:The Axiom of Infinity by Ferrotin on Wednesday December 07, 2022 @12:31AM (#33890946)

I remember being a kid and having this discussion in elementary school. Kids have enough intuition to know that operations with fractions should get the same result as with decimal numbers. Or that 1-0.999… = 0.000…. Or that different lengths have a length in between them. All are legitimate and compelling arguments.

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Re:The Axiom of Infinity by amelius on Wednesday December 07, 2022 @06:20AM (#33893118)

I think lots of students get lost with different orders of infinity (countable, uncountable, etc.), so I think there is definitely a point beyond which you can't push the intuition behind infinite objects.

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Re:The Axiom of Infinity by naasking on Wednesday December 07, 2022 @10:11AM (#33895195)

> Or that different lengths have a length in between them. All are legitimate and compelling arguments.

Except that's wrong, not all lengths do have a length between them.

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