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Apr
6
comment Let $A^{27}=A^{64}=I$, show that $A=I$
This is a great way to understand the Euclidean algorithm!
Mar
27
answered All natural numbers are equal.
Mar
26
comment How to show $(1/n!)^{1/n}$ goes to $0$ as $n$ goes to infinity?
I guess it's basically the proof from Ofir's answer. The interesting thing about this one is that you can get it easily just from the definition of $\ln{x}$ as $\int_1^x{\frac{dt}{t}}$. My professor showed us it as part of deriving facts about exponentials and trig functions from the base definitions. The 4 comes from the fact that you can easily show that $\ln(4) > 1$ just from the integral definition of $\ln$ and a simple Riemann sum argument.
Mar
26
comment How to show $(1/n!)^{1/n}$ goes to $0$ as $n$ goes to infinity?
Oh, sorry, I remembered wrong. The bound is $(n/4)^n\geq n!$. It comes from taking $\ln$ of both sides (I can put the proof in an answer if you are interested).
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.