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Jun
21
comment How should one picture a topology/ topological space?
Section 2 of arxiv.org/abs/1408.3887
Jun
21
answered How should one picture a topology/ topological space?
Jun
16
comment Homotopy/fundamental group question: Why group axioms fail when defined on paths?
@ThomasAndrews of course, a monoid. Thanks (corrected). I changed the wording of the opening phrase to better explain the purpose of this answer.
Jun
16
revised Homotopy/fundamental group question: Why group axioms fail when defined on paths?
added 250 characters in body
Jun
16
comment Homotopy/fundamental group question: Why group axioms fail when defined on paths?
absolutely @ThomasAndrews I just thought it useful for OP to understand that it is not the desire to have a group that brings us to quotient by homotopy, it is the quotient that interests us. I remember as a student that the motivation for the fundamental group was presented as if we just really are looking for a group and follow our nose to do what it takes to obtain a group. This is misleading and the reason for my lengthy answer which, as you say, subsides OP's question, but, hopefully, places it in a different light.
Jun
16
answered Homotopy/fundamental group question: Why group axioms fail when defined on paths?
Jun
11
reviewed Approve Composition of an injective and surjective function
Jun
10
comment a curve does not need to be injective?
yes @Mathcho, exactly.
Jun
10
answered a curve does not need to be injective?
Jun
9
comment Definition of a Cartesian Closed Category
@KevinCarlson you don't have to say what they are, but what OP did is not just not say what they are, but used a strange notation. I agree, this is probably just an interpretation of the wiki page stated, for whatever reason, using logical symbols. Obviously, if OP does not know what products and exponentials are, he should find out. That did not seem to be the question though.
Jun
9
comment Definition of a Cartesian Closed Category
en.wikipedia.org/wiki/Cartesian_closed_category
Jun
9
comment Definition of a Cartesian Closed Category
you can find the conventional notation in plenty of sources.
Jun
9
answered Definition of a Cartesian Closed Category
Jun
9
comment Version of the Axiom of Induction for Real Induction?
It's not clear what your question is. Of course you can state the principal of real induction (as appearing in the article you quote) using logical symbols and notation, much like you can do with any well-formed notion in mathematics.
Jun
9
comment Version of the Axiom of Induction for Real Induction?
I'm not sure what else you want then. The article you quote proves that what is called there the principal of real induction is equivalent to the completeness property (it even goes further to prove the same for general ordered sets). It is a restatement of some standard proof techniques in $\mathbb R$ and other posets.
Jun
9
answered Version of the Axiom of Induction for Real Induction?
Jun
9
comment Word in English to mean “study the convergence / divergence” of a series?
"study the nature of the series" is a perfectly valid English sentence, conveying what you explain (though it is not limited just to convergence issues. Just like the French word implies, it can also mean to study if the series is converging fast or slow, if it is positive or alternating, etc.).
Jun
9
answered Proving triangular inequality in general
Jun
9
comment Let $G$ be a finite group, $ord(G)=p^2$ ($p$ is a prime) prove that there is a subgroup of order $p$ in $G$
If you did not learn Cauchy's theorem yet, how come you are attempting to use Sylow???
Jun
9
answered Let $G$ be a finite group, $ord(G)=p^2$ ($p$ is a prime) prove that there is a subgroup of order $p$ in $G$