the 8/2(2+2) crowd is almost as annoying as the people who claim that 9.99999... and 10 are different numbers and equally annoying as the people who can't grasp that dividing by zero is as invalid in algebra as it is in arithmetic send tweet
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Interesting. Not sure if I'm missing something here, but 11.0000... obviously is rational. Therefore, as far as I understand this, it's not assuming that 10.1111... and 11.0000... are different. Instead, it's assuming that we never encounter such numbers.
Okay, I read it again.. :) I'd need to know more about the problems studied here, but assuming that natural numbers are irrational intuitively screams huge bag of problems. I trust that it's not an actual problem in this case.
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Yeah, it's only an issue when you want to have a set of positive measure to show a binary string in ML-Random, or when you want to work on subshifts (sets closed under the 'shift left one' operation) and need everything to be distinct points without such identities creeping in.
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e.g. forbidden word problems. If 0.101111... and 0.110000... are the same, then it's difficult to say that the first avoids the forbidden word '000' if the second is in some way identical to it. (just an ex. off the top of my head)
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