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this is a good example of a math education thing where i feel like people have real actual objections that are philosophical in nature that get stomped on and gaslit away with the raw mathematics. but the raw mathematics doesn't directly address the philosophical question https://t.co/6PulRMdMeL
people insisting that 0.999... can't possibly be equal to 1 is one of the most common math debates on the internet, it constantly recurs over and over and over again, and the temptation if you have a certain amount of math education is to just tell those people they're wrong
this is a total failure to take the objection seriously. imo it's an attempt to articulate a question. that question is: *what is a number*? what could it possibly mean for a number to have infinitely many digits, and what does it mean for two such numbers to be *the same*?
blasting someone with a formal definition of the real numbers (and then of what an infinite sum is, to formalize what is meant by "...") is *not* an answer to this question; the claim that the real numbers captures *what a number is* requires *philosophical* justification
generally speaking there's a shocking amount of gaslighting in math education https://t.co/gBlSgh1H6u
@QiaochuYuan while we're on the topic of math education philosophy, hank green released a nice video https://t.co/JMNxI1Ntna