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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
$<p>$ 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