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 Yearling
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Aug
30
comment A way to calculate e?
Though it is only described as having been "arrived at numerically by investigating the behavior of numbers that have been raised to their own power," it is worth noting this way to calculate e can be found here as #4 Power Ratio Method. (Citation: H. J. Brothers and J. A. Knox, New closed-form approximations to the logarithmic constant e, Math. Intelligencer, 20 (1998), 25-29.)
Aug
29
revised When is $(a+b)^n \equiv a^n+b^n$?
Corrected spelling to eliminate grammatical error and maintain consistency with linked wikipage.
Aug
28
comment Is the intersection of the following closed and open set closed? Generally?
@manofbear Good point! Sorry for the brain freeze. I've changed $F$ to be a closed subset of $\mathbb{R}$ that contains $B_{n}(0)$; in such a case, their intersection will always be $B_{n}(0)$, which is open by assumption hence provides a counterexample. (In my answer, I use the open ball of radius $1$.)
Aug
28
revised Is the intersection of the following closed and open set closed? Generally?
Switched F for something much wiser!
Aug
28
comment Strategy for reading math books, is it better to prove the theorems yourself or just read them?
You might check my answer in MESE 2164 which includes a sample page of questions to ask oneself for someone just starting with Munkres' text. (The other responses there may be helpful, as well!)
Aug
28
answered Proving that $a^{b}$ is rational (Elementary number theorey)
Aug
28
revised Is the intersection of the following closed and open set closed? Generally?
added 3 characters in body
Aug
28
answered Is the intersection of the following closed and open set closed? Generally?
Aug
28
answered When is $(a+b)^n \equiv a^n+b^n$?
Aug
28
comment When is $(a+b)^n \equiv a^n+b^n$?
Also, unexcitingly, for $n=1$.
Aug
24
revised Is this an instance of any existing convex pentagonal tilings?
Fixed link; also changed 'his' to 'this'
Aug
23
revised Guessing how many times a smaller number goes into bigger number
Corrected approximation.
Aug
23
answered probability problem: train line
Aug
23
answered Guessing how many times a smaller number goes into bigger number
Aug
16
comment Mental Calculations
+1 for similarity of thought! I also look at the ones places and think, I can pair $11^2$ with $13^2$, and $12^2$ with $14^2$...
Aug
15
comment Can a sequence have infinitely many limits among its subsequences?
@ASCIIAdvocate Yes, and the re-naming could be accomplished by the bonus listed at the end. My response is mostly to indicate yet another way of thinking about the question and its answer; similarly, though dove-tailing is often used to enumerate the positive fractions, one could accomplish the same by listing $a/b$ ordered first by $a+b<n$ as $n$ increases, and, if $a+b = c+d$, listing $a/b$ before $c/d$ provided $a<c$. The enumeration begins: $1/1,1/2, 2/1, 1/3, 2/2, 3/1, \ldots$ (I believe that multiple ways of thinking about the problem and an answer produce a deeper understanding.)
Aug
14
revised Advice on finding counterexamples
The *group* isn't divisible by a number; its *order* is... so I added the word order.
Aug
14
answered Can a sequence have infinitely many limits among its subsequences?
Aug
14
answered How to prove that $4^{2n}-1$ is divisible by $3$ or $5$
Aug
3
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