Jon
Reputation
Top tag
Next privilege 2,000 Rep.
 Aug10 comment Is there a way to pick a $k$ such that $p_0p_1 + ik$ is always a product of two primes? $p_0p_1+(p_0p_1)k = p_0p_1 (1 + k)$, no? Jun16 awarded Enthusiast Jun11 accepted Combinatorial proof that binomial coefficients are given by alternating sums of squares? Jun11 comment Combinatorial proof that binomial coefficients are given by alternating sums of squares? Very nice! (characters...) Jun11 asked Combinatorial proof that binomial coefficients are given by alternating sums of squares? Feb11 comment If a product of relatively prime integers is an $n$th power, then each is an $n$th power Have you considered the prime factorizations of $a$, $b$, and $c$? Feb9 revised Can someone explain how this question is reduced using basic postulates add info on p6b Feb9 answered Can someone explain how this question is reduced using basic postulates Feb8 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. Jan17 awarded Nice Answer Jan16 awarded Commentator Jan16 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. Jan16 answered Why do we need to prove $e^{u+v} = e^ue^v$? Jan16 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. Jan16 comment Why do we need to prove $e^{u+v} = e^ue^v$? How is the function $e^x$ defined in the text? Jan10 awarded Scholar Jan10 accepted Topic for a high school-level math elective? Jan10 comment Topic for a high school-level math elective? Great info. Thanks! Jan10 awarded Nice Question Jan8 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.)