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seen Apr 3 at 18:27

Jan
10
awarded  Scholar
Jan
10
accepted Topic for a high school-level math elective?
Jan
10
comment Topic for a high school-level math elective?
Great info. Thanks!
Jan
10
awarded  Nice Question
Jan
8
comment Topology of the power set
@t.spero: Xiaochuan is using the product topology on $2^{[0,1]}$. (The reference to Tycohoff's theorem is a clue!) More information is available on wikipedia. In concrete terms, if your base set is $S$, open sets on $\mathcal{P}(S)$ are generated by the sets $\mathcal{U}(F, G)$ for finite sets $F$ and $G \in S$, where $\mathcal{U}(F,G)$ is defined to be $\{U \subset S : F \subset U \text{ and } G \cap U = \emptyset\}$. (I believe I have that right, but I am also tired, so no guarantees.)
Jan
8
answered Topology of the power set
Jan
8
awarded  Student
Jan
8
awarded  Editor
Jan
8
revised Topic for a high school-level math elective?
edited title
Jan
8
asked Topic for a high school-level math elective?
Dec
26
comment Arithmetic on $[0,\infty]$: is $0 \cdot \infty = 0$ the only reasonable choice?
Note that the "useful proposition" that is given on the next page (namely "If $0 \leq a_1 \leq a_2 \leq \cdots$, $0 \leq b_1 \leq b_2 \leq \cdots, a_n \to a \text{ and } b_n \to b, $ then $a_nb_n \to ab$") only holds if $0 \cdot \infty$ is defined to be $0$.
Dec
24
comment Optimal algorithm for finding the odd spheres
Do we know in advance whether the odd sphere is heavier or lighter than the others?
Dec
19
comment Set Theoretic Definition of Numbers
You might find this "buzz" by Terence Tao useful: google.com/buzz/114134834346472219368/RarPutThCJv/…
Dec
19
awarded  Critic
Dec
17
comment Easy question about finite energy due to convergence
@Fulwig: there are many ways to understand that identity, but I think the easiest is to note that the LHS is an infinite geometric series. Wikipedia has more: en.wikipedia.org/wiki/Geometric_series
Dec
16
answered solving integral $\int{{3^x}{e^x}dx}$
Dec
15
answered Count of unique algebras with one unary operation (on finite set)
Dec
15
awarded  Supporter
Dec
15
answered Do your friends on average have more friends than you do?
Dec
14
comment Why do we define quotient groups for normal subgroups only?
This doesn't fix the problem. See Tobais's answer. No matter how we look at the group operation, it has to be independent of which coset representatives we choose. The problem is easiest to see if you just consider the product $(xh)(yh)$ like I do above, but expand Tobais's $(xy)H=(x'y')H$ and you'll still get a term like $y^{-1}hyh$ which needs to be in $H$. Therefore $H$ must be normal.