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Dec
3
answered Noncyclic group has at least 5 subgroup
Dec
2
answered Prove the set of vectors of norm one is compact
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.
Dec
2
answered Is the Cartesian product of sets associative?
Dec
1
answered How do I prove that among any $5$ integers, you are able to find $3$ such that their sum is divisible by $3$?
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
22
answered Do complex roots always come in pairs?
Nov
15
answered Is infinite binary operation for zeros 0+0…+0 well defined math object?
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
answered Equivalent definitions of a completely regular space
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
Nov
10
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