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Feb
9
answered Can someone explain how this question is reduced using basic postulates
Feb
8
comment No prime number between number and square of number
Bertrand's postulate guarantees the existence of a prime between $n$ and $2n$ for all integers $n > 1$. Therefore there are no non-trivial examples of the phenomenon you describe.
Jan
17
awarded  Nice Answer
Jan
16
awarded  Commentator
Jan
16
comment Why do we need to prove $e^{u+v} = e^ue^v$?
@bobobobo In that case, we have no a priori information about the function $e^x$, and we've got to establish its basic properties from the definition provided.
Jan
16
answered Why do we need to prove $e^{u+v} = e^ue^v$?
Jan
16
comment Why do we need to prove $e^{u+v} = e^ue^v$?
It's also quite common to define $ln(x)$ as the integral $\int_1^a \frac{1}{x} \, dx$, which might be the case here.
Jan
16
comment Why do we need to prove $e^{u+v} = e^ue^v$?
How is the function $e^x$ defined in the text?
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?