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Don't have much time these days...


Mar
12
comment show that the limit of $\lim_{n \to \infty} n^{\frac{1}{n}} = 1$
@FH93: One suggestion, please try to pick a question which itself isn't closed as a dupe. Perhaps it should be a feature of this site...
Mar
12
revised Subset Sum problem computational complexity
remove computational-complexity which is more theoretical.
Mar
12
comment Subset Sum problem computational complexity
It the integers can get large ($2^{63}$), then you are probably out of luck for such a huge set.
Mar
12
comment How can I explain to my professor his argument invokes the AC?
I might well be, no argument about that. The definition talks about existence of a ball (rather than a set of balls), you take that ball, and take its radius. I might be implicitly invoking AC here, and is one reason I gladly accept AC :-) Looking forward to the answers here, thanks for asking this.
Mar
12
comment How can I explain to my professor his argument invokes the AC?
I meant that the definition already provides you a choice function. So there is no invocation of AC going on.
Mar
12
comment why we say this function have closed form while the other doesn't?
Depends on your definition of closed. See: math.stackexchange.com/questions/265780/…
Mar
12
comment How can I explain to my professor his argument invokes the AC?
No. By definition a choice function exists, isn't it? But, I am no expert on set theory.
Mar
12
comment Subset Sum problem computational complexity
There are pseudo polynomial time algorithms too. Did you check out the subset sum wiki?
Mar
11
comment Division of Factorials
@wlod: :-)......
Mar
9
comment Computing the unit digit
You mean unit digit of the integer part of that thing?
Mar
8
revised Intuitive proofs that $\lim\limits_{n\to\infty}\left(1+\frac xn\right)^n=e^x$
added 11 characters in body
Mar
8
comment Intuitive proofs that $\lim\limits_{n\to\infty}\left(1+\frac xn\right)^n=e^x$
@ThomasAndrews: Thanks for pointing out that this intuition can lead to wrong results. We need proof and cannot leave it as a bare statement, I agree with you. But, is your claim that this intuition cannot be turned into a proof for this problem? Note that the original problem was to find "intuitive proofs" that the function is exponential. I would say that this answer qualifies, irrespective of whether the intuition used leads to wrongs results in some cases.
Mar
8
comment Intuitive proofs that $\lim\limits_{n\to\infty}\left(1+\frac xn\right)^n=e^x$
@ThomasAndrews: This isn't supposed to be rigorous. Just intuitive...
Feb
28
awarded  Nice Answer
Feb
27
awarded  Nice Answer
Feb
10
comment Showing $\sum_{n\in\mathbb{N}}\frac{\Lambda(n)}{n}=\log (x)+O(1)$ using a given result.
Have you tried applying Abel's identity? For an example (and a reference to Abel's identity) see here: math.stackexchange.com/a/12588/1102
Jan
30
awarded  Nice Answer
Jan
22
comment Proof that $x^2+4xy+y^2=1$ has infinitely many integer solutions
@Vishwa: The equation $a^2 - 3b^2 = 1$ has infinitely many solutions. Now $y=b$, $x = a -2b$ and you are done, aren't you?
Jan
17
awarded  limits
Jan
16
comment Solving the integral $\int_{0}^{\infty} \frac{\sin{x}}{x} \ dx = \frac{\pi}{2}$?
@Ale: I believe cardinal said that... There might be different versions of Fubini (I am not aware of though...)