Yeah but because you can't see at that level of precision you don't know what those numbers are
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Ever since this debate became an Internet meme there's been mathematicians pointing out that *you don't have to* accept this if you don't want to You don't have to do anything, in math, math is a construct you choose to adopt for your own purposes
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Your whole "equivalent to but not equal" thing, for instance, is a matter of much discussion - the = sign does indeed mean different things to different people at different times It's valid, you can say that if you want
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Well, 1.0... 1 isn't necessarily precisely defined
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Or, incredibly informally, by asking what 1-0.999999.... equals.
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The problem with that is people not understanding infinity going 0.0...1, implying there's a one after the infinite sequence of zeroes.
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My math class are far away but, the way I interpret that is : as 0.3333... is exactly 1/3, 0.9999... is exactly 3/3, or 1.
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Yeah but that's not a rigorous proof because you haven't actually proven that 0.3333... is 1/3 either What this fight is about at heart is whether you're "allowed" to write numbers with that "..." after them and talk about an infinite series of digits
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