2h
comment Solution for congruence mod $p^2$
Oh, and in case you didn't think of it, you'd also have $a^2 + 1 = pd$ for some integer $d$.
2h
answered Solution for congruence mod $p^2$
3h
answered Why Not Define Connectedness to Mean Path Connected?
3h
comment Do Cantor's Theorem and the Schroder-Bernstein Theorem Contradict?
Literally. Noun. 1. in the most basic sense without metaphor. 2. metaphorically.
5h
comment Find $\bigcap_{n=1}^\infty(0,1/n)=\emptyset$
I'm not sure what you've written makes sense. Can you write it more clearly and precisely, and elaborate upon how you're trying to argue?
6h
answered The field closure of a countable union of countable fields is countable?
6h
answered the letters abcdefgh are to be used to form strings of length 5. How many strings contain the letter a if repetions are allowed?
6h
comment Proof $x=\sin(x+1)$ has one solution in $\mathbb{R}$
@Peter: While that shows existence, it doesn't show uniqueness. The OP sounds like he's asking how to show uniqueness, although it is worth pointing out that he hasn't yet shown existence!
6h
answered Proof $x=\sin(x+1)$ has one solution in $\mathbb{R}$
18h
comment On inversive geometry
@Mainviel: Well, have you yet plugged in the formula for $i_K$ into the two conditions you're trying to prove? I assumed you had done that already but opted not to post it, and were having trouble with the algebra.
18h
answered On inversive geometry
1d
comment Is a continuous function on $(a,b)$ also continuous on $[a,b]$?
@vadim: The question doesn't look poorly asked at all! It's just asking to crowdsource an assignment, rather than being about mathematics with the scope defined in the help center. (I suppose it's poorly asked if the intent wasn't actually to crowdsource the assignment)
1d
answered Proof that $f(x)=\frac{(\sin x)^3}{x}$ gets maximum in $(0,\infty)$.
1d
comment understanding the meaning of formal linear combination and tensor product
Right. A useful notational device is, for $s \in S$, to let $[s] \in \mathbf{R}[S]$ denote the corresponding vector (you might use angle brackets rather than square brackets, based on your notation). In the case that $S$ is a vector space itself, this device lets us easily distinguish between $a+b \in S$, $[a+b] \in \mathbf{R}[S]$, and $[a] + [b] \in \mathbf{R}[S]$. Or similarly if $r$ is a scalar, we can easily tell apart $r[a]$ and $[ra]$.
1d
comment understanding the meaning of formal linear combination and tensor product
Adding appropriate line breaks would make it much easier to read your post.
1d
answered understanding the meaning of formal linear combination and tensor product
1d
comment Preimage of 0 for a differentiable function.
I bet the complication comes from considering an arbitrary manifold rather than just $\mathbf{R}^n$.
1d
comment Determine how real parameters a,b,c are ordered
For the record, the voting was three "off-topic" and two "unclear what you're asking".
1d
comment Preimage of 0 for a differentiable function.
IMO it is somewhat intuitive, once you think of the distance function $$d(x, A) = \inf_{y \in A} d(x,y)$$ You just need to plug it into something to smooth out the kink on the boundary; e.g. squaring the distance if you just want it to be once differentiable. Or am I totally wrong and this doesn't work?
1d
comment Should word problems be reasonable?
I once obtained the result that the mass of an object was negative. However, this was not a word problem: this was the analysis of an actual experiment I did in chemistry class. And despite being unreasonable, it was the correct answer to give, based on the measurements recorded during the experiment.
1 2 3 4 5