Re:The Axiom of Infinity
by Ferrotin on Tuesday December 06, 2022 @11:22PM
(#33890602)
Calling “0.999… = 1” very unintuitive is a very strange thing to say, because that makes perfect sense to most children. I’d like to see a result that truly is unintuitive, like what we get with the axiom of choice.
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> Calling “0.999… = 1” very unintuitive is a very strange thing to say, because that makes perfect sense to most children.
Gotta call bullshit on that. First I don't think you have any robust empirical data on that question.
Second what's convincing to children that don't have enough knowledge of math to have formed any intuitions about it is not a compelling argument.
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.
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.