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Results tagged with gm.general-mathematics
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user 1176
Questions about mathematics which don't fall into the other arXiv categories. If you have a general question about mathematics but it is not research level, it's off-topic but it might be welcomed on Mathematics Stack Exchange.
20
votes
Situations where “naturally occurring” mathematical objects behave very differently from “ty...
In practice, subsets of $\mathbb{R}$ encountered in analysis tend to be measurable, but not all subsets of $\mathbb{R}$ need be measurable, and in fact are not by the Axiom of choice.
In practice, p …
91
votes
Accepted
Is rigour just a ritual that most mathematicians wish to get rid of if they could?
I was not going to write anything, as I am a latecomer to this masterful troll question and not many are likely going to scroll all the way down, but Paul Taylor's call for Proof mining and Realizabil …
30
votes
What would remain of current mathematics without axiom of power set?
Words are not magic. Just because you have given something a name it does not necessarily exist, and conversely, a thing may exist without having a name.
Let me explain this. You say that the powerse …
- 48.8k
2
votes
If a continuous function is differentiable at a point, is it differentiable in some neighbor...
The answer is negative. Take a bounded nowhere differentiable continuous map $f : \mathbb{R} \to \mathbb{R}$ and consider the map $g(x) = f(x) \cdot x^2$, which is differentiable at $x = 0$, but not a …
- 48.8k