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Sep
3
comment Question about initial value problem
I suspect that there is a missing pair of brackets (or parentheses if you will) in the differential equation: shouldn't it be $\frac{dy}{dx}=(1-2x)/y$?
Sep
3
answered Question about initial value problem
Sep
2
awarded  Yearling
Dec
21
comment Isomorphism and direct product of groups
Isn't $\mathbb{Z}_{mk}$ always cyclic? ;)
Dec
11
comment What are a few examples of noncyclic finite groups?
Indeed it's not restricted to finite groups: every group $G$ acts by (e.g.) right multiplication on itself, giving an embedding of $G$ in the symmetric group on $G$.
Sep
13
revised $\ln(-1) - \ln(-2)$ is it definable or have answer?
replaced x\geq 0 by x>0
Sep
13
suggested suggested edit on $\ln(-1) - \ln(-2)$ is it definable or have answer?
Sep
2
awarded  Yearling
Aug
26
answered An exercise in logic
Jul
19
comment $ρ_ωG$ is a subgroup of $ρG$ containing $G$.
Maybe you could tell us what the Rajkov completion is?
Jul
3
revised Is this true? $f(g(x))=g(f(x))\iff f^{-1}(g^{-1}(x))=g^{-1}(f^{-1}(x))$.
Added clarification
Jul
3
answered Is this true? $f(g(x))=g(f(x))\iff f^{-1}(g^{-1}(x))=g^{-1}(f^{-1}(x))$.
Jun
17
answered Relation between differentiable,continuous and integrable functions.
May
24
comment A 2nd countable metric space is separable
@AsafKaragila Ah, indeed. I somehow managed not to see the word `metric' in my haste.
May
24
comment A 2nd countable metric space is separable
Regarding the converse: there are spaces that are separable but not second countable. See en.wikipedia.org/wiki/Lower_limit_topology for example.
May
20
awarded  Constituent
May
20
answered Reference request for ordered groups
May
19
comment Using induction to verify a statement
$\sum_{k=1}^n(k+1)^2=2^2+\cdots+(n+1)^2$, while $\sum_{k=1}^{n+1}k^2=1^2+\cdots+(n+1)^2$.
May
19
comment Using induction to verify a statement
Agreed that $P(k)$ has not been proven (at the point it's stated) and that $P(k+1)$ is a statement of what we need to prove. And agreed that it's often a good idea to spell these things out. My (first!) quibble was only that the notation $P(k)$ is playing two roles.
May
19
comment Using induction to verify a statement
A further quibble: the roles of $k$ and $n$ appear to be mixed up: there's an $n$ on the left-hand side of your first equation but only a $k$ on the right-hand side. Also, the left-hand side of the `$P(k+1)$' statement should be something like $\sum_{m=1}^{k+1}m^2$, not $\sum (k+1)^2$