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Oct
23
comment What can you say about $f$ and $g$ in the case that $fg$ is 1) Injective, 2) Surjective - Cohn - Classic Algebra Page 15
Yup. If you expanded out why the statements you claim are true (especially the $x_1fg \neq x_2fg$ proof, I think I know what you are getting at but you are missing details) it would be more clear that you proved that $f$ is injective two different ways.
Oct
23
comment What can you say about $f$ and $g$ in the case that $fg$ is 1) Injective, 2) Surjective - Cohn - Classic Algebra Page 15
@Committingtoachallenge You basically have it now and adding the small change I see you added made it far more clear than it was before. Are you trying to prove injectivity two different ways? It looks like you basically have two proofs which may have also been a tad confusing.
Oct
23
revised What can you say about $f$ and $g$ in the case that $fg$ is 1) Injective, 2) Surjective - Cohn - Classic Algebra Page 15
added 6 characters in body
Oct
23
answered What can you say about $f$ and $g$ in the case that $fg$ is 1) Injective, 2) Surjective - Cohn - Classic Algebra Page 15
Oct
23
revised What can you say about $f$ and $g$ in the case that $fg$ is 1) Injective, 2) Surjective - Cohn - Classic Algebra Page 15
Number theory does not belong.
Oct
23
suggested suggested edit on What can you say about $f$ and $g$ in the case that $fg$ is 1) Injective, 2) Surjective - Cohn - Classic Algebra Page 15
Oct
23
comment The behavior of quotient groups under homomorphisms
Awsome! Glad to help.
Oct
22
answered The behavior of quotient groups under homomorphisms
Aug
6
comment How “bad” can presentation of the trivial group get?
@BabakS. I don't think that would be appropriate for this particular question. I suspect that a well phrased and motivated big list question could be asked looking for interesting presentations of the trivial group, and where these presentations came from (like answered some question in topology or something), though (if it hasn't been done before).
Jul
2
awarded  Curious
Jun
4
comment Looking for a field isomorphic to $\Bbb{Q}$
Let $\alpha: \mathbb{Q} \to \mathbb{N}$ be a bijection and define operations $\times_\alpha, +_\alpha$ on $\mathbb{N}$ so that $\alpha$ is an isomorphism of fields. Your question should be more specific and well defined, otherwise I would not be surprised if your question is closed.
May
18
comment Conjecture on OEIS A167055
How high have you not disproved the conjecture?
May
14
answered Functional equation $f(x)=f(\sqrt{x})$
Apr
14
awarded  Yearling
Mar
18
awarded  Disciplined
Mar
16
accepted How many normal subgroups of the free group on $n$ generators?
Mar
15
asked How many normal subgroups of the free group on $n$ generators?
Mar
13
comment Can $\mathbb R$ be enumerated after all?
In bijection with some ordinal(that is uncountable), not the natural numbers.
Mar
9
comment Let $A$ be a subset of $C$ and $B$ a proper subgroup of $C$
@DonAntonio Okay, I was thinking you were going to do some something with reverse inclusion ($A \leq B$ iff $B \subseteq A$) and see if, with the help of Zorn's lemma get a much smaller set than $C \setminus B$ (which would be maximal with the subset relation). As for the hint $Bc$ and $c^{-1}B$ are disjoint from $B$. The idea would be to pick a $ b \in B $ and an element from $Bc$ and one from $ c^{-1}B $ that multiply to get $b$.
Mar
9
comment When should I start learning Set Theory?
This question will be useful and may answer it for you. I think most of the really important stuff showed up in the answers to your question (some basics on cardinals, ordinals, and well ordering principle/axiom of choice) and I think that can be picked up as you go along. Although, if you want to study set theory or foundations of mathematics then you probably could start now.