Well /sci/? I mean A can be taken out of the question immediately

>>8922164
0.999... is the same as 1, so not valid. and c and d are both nonsensical, as you cant have a final digit after an infinite number of 9's, so theyre probs the same as 1, too. so none of them

>>8922164
C) Because B) is 1 so its not on the set, and no C) != B) Because C is finite so is not equal to 1

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>>8922164
[math]\sup [0,1) = 1 [/math]
[math]\text{But }1 \not \in [0.1) \text{, so A is not the answer}[/math]
[math]0.999\dots = 1 \text{, so B is not the answer } [/math]
[math]0.999\dots9 < \frac{(0.999\dots9) + 1}{2} \in [0,1) \text{, so C is not the answer}[/math]
[math]\text{D is not the answer by the same reasoning }[/math]

>>8922164
0.(9)

>>8922164
1-ε

>>8923106
0.(((9)))

>>8923100
>(((Axiom of completness)))

>>8923148
any founded problems with that?

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>>8923161
Nonstandard analysis is fully expressible in terms of ZFC (it just makes heavier use of C), so it's as consistent as modern mathematics is.

2(0.999...) - 1

>>8922164
The question is wrong. There is by definition no maximum in [0,1). The supremum is 1 though.

>>8923371
No way, nonsensical questions to trigger brainlets on my /sci? Unheard of.