Ittay Weiss
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93/100 score
 Sep 16 comment motivation of definition of semigroup it's a practical issue. Lots of things are not groups but they are semigroups. Sep 16 answered Why the surface of the sphere is not a Euclidean space? Sep 15 comment Prove the completeness of the real numbers exactly. It's a mystery. Sep 15 comment Prove the completeness of the real numbers @MichaelHardy you may be right. I don't know. It's a bit of guess work what OP had in mind. E.g., which construction of the reals he is working with as it appears he is interested in some detail of a construction. I don't know. In any case, the density of the rationals is typically rather easy to show while metric completeness is harder. Again, who knows... Sep 15 answered Prove the completeness of the real numbers Sep 15 answered On an equivalence of definitions of a transitive set. Sep 12 comment Understanding Closure, examples and while I didn't check I doubt there is a topology book written by Munkres and by Muncres. Sep 12 comment Understanding Closure, examples @AnthonyColombo I think you should stop for a minute and figure out why in the Euclidean topology on $\mathbb R$ the closure of $(a,b)$ is $[a,b]$. It will sort things out for you. Sep 12 comment Understanding Closure, examples @PedroTamaroff the smallest set in that collection need not a-priori exist. Sep 12 answered Definition of neighborhood Sep 11 comment Proving that a minimal spanning set is linearly independent why do you assume $S$ is finite? Sep 9 awarded Good Answer Sep 9 awarded Nice Question Sep 2 comment Quantifiers and Mathematical Modelling and what do you call the $x$, $y$, $\varepsilon$, and $S$ in what I wrote above? Sep 2 revised How to show that any non-trivial subgroup of G is cyclic added 12 characters in body Sep 2 comment How to show that any non-trivial subgroup of G is cyclic  is meaningless since $p$ is a number, not an element of $G$. The solution is staring you in the face right now, you just need to collect your thought. Look at the my answer. $H$ is an arbitrary non-trivial subgroup. Its order is prime. Every group of prime order is cyclic. So, what can you say about $H$? Sep 2 revised Quantifiers and Mathematical Modelling edited body Sep 2 comment How to show that any non-trivial subgroup of G is cyclic @DerekHolt some texts define it differently and unfortunately things are not always consistent. In this case, it is clear from the content of the question what is meant. Sep 2 answered How to show that any non-trivial subgroup of G is cyclic Sep 2 answered Quantifiers and Mathematical Modelling