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Mar
24
comment How to show $(1/n!)^{1/n}$ goes to $0$ as $n$ goes to infinity?
I believe if you replace $e$ with 2 in the inequality, you can prove this without integration.
Mar
22
answered What was the first bit of mathematics that made you realize that math is beautiful? (For children's book)
Mar
22
comment What was the first bit of mathematics that made you realize that math is beautiful? (For children's book)
Actually, the one that's interesting is the sum of the first $n$ odd integers.
Feb
15
awarded  Necromancer
Feb
12
comment Find five positive integers whose reciprocals sum to $1$
Ah, missed that.
Feb
12
comment The kernel of a continuous linear operator is a closed subspace?
Wouldn't your argument about a convergent subsequence just imply that ker L is not compact, not open?
Feb
12
comment Find five positive integers whose reciprocals sum to $1$
I think it's less than $n!$ if you still consider $\frac{1}{2} + \frac{1}{2}$ and $\frac{1}{2} + \frac{1}{2}$ to be the same.
Feb
12
comment The kernel of a continuous linear operator is a closed subspace?
You don't need to assume that $L \neq 0$. If $L = 0$, then it is automatically continuous, and the kernel, the whole space, is closed.
Jan
19
awarded  Nice Question
Jan
1
awarded  Nice Question
Dec
24
comment Purely “algebraic” proof of Young's Inequality
@AndresCaicedo excellent blog post!
Dec
23
awarded  Nice Question
Dec
20
comment Does the number pi have any significance besides being the ratio of a circle's diameter to its circumference?
Maybe that has something to do with angles and the 2D lattice.
Dec
20
comment Working out digits of Pi.
Suit yourself, but do take a read of math.stackexchange.com/faq#editing.
Dec
20
reviewed Reviewed How do I implement an induction argument to show that we may assume that a partition $Q$ of $[a,b]\in{R}$ which refines $P$ has only one more point?
Dec
19
comment Axiomatic characterization of the rational numbers
Somehow, it seems more elegant to define it as having characteristic 0 and deriving that it is ordered rather than the other way around.
Dec
19
comment Axiomatic characterization of the rational numbers
Saying that a field is not complete is not sufficient. There are lots of fields that are not complete, whose completion is $\mathbb{R}$. $\mathbb{Q}$ and $\mathbb{Q}(\sqrt{2})$ are two trivial examples.
Dec
18
comment Working out digits of Pi.
Which mathematician?
Dec
18
comment Is there a fundamental reason that $\int_b^a = -\int_a^b$
In case anyone is wondering, we are going to go with the Karr convention. The reason is that it's the only one that's consistant with computing a summation with symbolic limits and then substituting a numerical value vs. computing the summation with the numerical value to begin with, where the numerical value gives reversed limits. This also provides a good argument for integrals (in terms of the Fundamental Theorem of Calculus).
Dec
18
revised Working out digits of Pi.
Give the series explicitly