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Feb
8
comment Category-theoretic description of the real numbers
@goblin I'm not quite sure what you are asking.
Jan
16
comment Any subspace of connected set is connected?
some consider $\emptyset$ to be not connected, nor disconnected, much like the status of $1$ and primality. The reason is that some theorem become a bit cleaner to state (e.g., a space is then the union of connected subspaces, uniquely up to an ordering of the subspaces).
Jan
12
comment Notions of groups acting on groups
Thanks @Thomas for the very clear answer.
Jan
4
comment Vector space that can be made into a Banach space but not a Hilbert space
ah, I understand your question now.
Jan
4
comment Vector space that can be made into a Banach space but not a Hilbert space
Which norms on $\mathbb R^n$ do you know? Every heard of the $\ell_p$ norm? If $p\ne 2$, then its not coming from an inner product.
Jan
4
comment How to pronounce mathematical words correclty
I would say that such questions do belong on this site.
Dec
21
comment Computer Science in mathematical setting
thansk @DavidRicherby I added 'complexity'
Dec
3
comment Noncyclic group has at least 5 subgroup
corrected. Thanks to both of you.
Dec
2
comment Find an example of metric space
Take $\mathbb R$ with the usual metric, and rename $0$ to "banana". So now $\lim 1/n$ is "banana" and clearly banana $\ne 0$.
Dec
2
comment Is the Cartesian product of sets associative?
@Abstraction what algebraic structure are you referring to?
Dec
2
comment Is the Cartesian product of sets associative?
not quite. In cartesian categories the product is not necessarily associative, and often, as in $Set$, it is not associative. The fact that in any discussion where isomorphism is synonymous with identity you can treat isomorphic objects as identical is a tautology, and has nothing to do with OP's question. Bringing in categories as an answer and not mentioning coherence misses the whole point I'm afraid.
Nov
29
comment What are some of best books in Galois theory?
Garner is also excellent. These two books in conjunction is how I learned the basics - and it was wonderful.
Nov
28
comment If functions compose both ways to make automorphisms, are they isomorphisms?
Yes, but the way you worded your answer hides the split part. You deduce monichood, epichood, and then isoness. But generally, monic+epic does not imply iso. Split monic+split epic does.
Nov
28
comment If functions compose both ways to make automorphisms, are they isomorphisms?
$g$ has a left inverse, so it's mono. $g$ has a right inverse, so it's epi. How do you conclude it's an iso?
Nov
25
comment If $f$ is differentiable and $f'(a)<0$, is $f$ decreasing on some interval around $a$?
Any Weierstrass function will do.
Nov
24
comment Methods of Evaluating $\lim_{x\rightarrow 0} \frac{\sin x}{x}=1$ Multiple Choice Question
option c) is nonsense, as with any claim to compute a limit by looking at the graph. Option d) may work just fine, if you define $\sin(x)$ by its Taylor expansion.
Nov
14
comment Probability that among 5 people, exactly 2 of them are born in the same month
The question can not be answered without making assumptions about the probabilities. The question probably wants you to assume equal probability for birth in each month. That assumption though is not true. This is a good example of a very poorly phrased question.
Nov
11
comment Equivalent definitions of a completely regular space
further adjust your function as required.
Nov
11
comment Are there any situations in which L'Hopital's Rule WILL NOT work?
You are absolutely right @HagenvonEitzen Somehow I was trying to guess what OP had in mind, and came up with that.
Nov
10
comment Are there any situations in which L'Hopital's Rule WILL NOT work?
you are very welcome @ErinAjello