Ittay Weiss
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 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 awarded Guru Nov 10 awarded Good Answer Nov 10 awarded Nice Answer Nov 10 revised Are there any situations in which L'Hopital's Rule WILL NOT work? added 19 characters in body Nov 10 comment Are there any situations in which L'Hopital's Rule WILL NOT work? I do not think OP was asking about the assumptions, but rather if the assumptions are met is it guaranteed using L'Hopitals will be successful. The answer is negative, but not because sometimes the conditions are not met. Nov 10 answered Are there any situations in which L'Hopital's Rule WILL NOT work? Nov 10 comment Are there any situations in which L'Hopital's Rule WILL NOT work? but the conditions for L'Hopitals' rule are not met. How does this answer OP's question? Nov 9 awarded Nice Answer