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7h
comment Do you paragraph a proof?
If you wrote a 5 (or even just two) page proof as a single paragraph I would not want to read your proof!
7h
comment Injectivity of Natural Homomorphism to Groupification
@Tunococ You're welcome. I'm glad I could help.
9h
revised Injectivity of Natural Homomorphism to Groupification
Added (likely) reference.
9h
answered Injectivity of Natural Homomorphism to Groupification
11h
answered Onto homorphisms from $S_4$ to $S_2$
1d
comment Proposition into spoken language
Pretty much; I'd add a comma after "that". You might also just say "It's not raining if and only if ...".
1d
revised Proposition into spoken language
Fixed LaTeX
1d
comment $C\subseteq D$. Prove $P_C$ is a subgroup of $P_D$.
If $C=\emptyset$, then $P_C = \{\emptyset\}\neq\emptyset$; i.e., a set with one element. As for the latter part, it sounds like you are assuming what you need to prove (that $P_C$ is indeed a group). You need to show that, if $X,Y\in P_C$ (i.e., if $X,Y\subseteq C$), then $X\triangle Y\in P_C$ (i.e., $X\triangle Y\subseteq C$).
1d
comment Proving the Derivative of $f'(x) = b^x$
Use the chain rule.
1d
answered $C\subseteq D$. Prove $P_C$ is a subgroup of $P_D$.
1d
comment $C\subseteq D$. Prove $P_C$ is a subgroup of $P_D$.
Hmm. Probably not. The way the question is worded suggests that $P_D$ is a group, and you are to show that its subset $P_C$ is a subgroup under the operation inherited from $P_D$. (Moreover, since the question asserts that this is true, why are you looking for a counter-example?)
1d
comment $C\subseteq D$. Prove $P_C$ is a subgroup of $P_D$.
Assuming symmetric difference is your operation, you just need to notice that the operation on $P_C$ is the same as on $P_D$, and then show that, for $X,Y\in P_C$, one has $X\triangle Y\in P_C$ (since each element is its own inverse).
1d
comment $C\subseteq D$. Prove $P_C$ is a subgroup of $P_D$.
To have a group you need not only a set of elements, but an operation on those elements. What is the operation on the power set of a set that makes it a group? (I would guess symmetric difference, since that works.)
1d
comment The range of $\arccos$
$\overline{\arccos(z)} = \arccos(\bar{z})$
1d
comment $C\subseteq D$. Prove $P_C$ is a subgroup of $P_D$.
So $P_X$ is the power set of $X$? And the operation is symmetric difference?
2d
revised Are there at least denumerably many distinct group operations on any denumerable set?
Fix corner case.
2d
comment Are there at least denumerably many distinct group operations on any denumerable set?
@whacka As I understood it, the question was to show there are at least countably many groups. Am I wrong?
2d
revised Are there at least denumerably many distinct group operations on any denumerable set?
Added more information.
2d
answered Are there at least denumerably many distinct group operations on any denumerable set?
Aug
20
answered Group of even order must contain $a:a=a^{-1}$ $ (a\not = e)$