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May
16
awarded  Good Answer
May
12
comment How to represent the floor function using mathematical notation?
With the note that the $\max$ is well-defined because the set is bounded from above (by $x$), and every set of integers bounded above has a maximum element by the well-ordering principle.
May
8
awarded  Caucus
Apr
26
asked Understanding a proof of Diaconescu's theorem
Apr
26
awarded  Nice Answer
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!