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seen Apr 15 at 12:51

Feb
6
answered What is the current status of Vinay Deolalikar's proof that P is not equal to NP
Feb
6
answered Linear Programming Books
Feb
6
answered about career choice
Feb
6
comment How to know that $a^3+b^3 = (a+b)(a^2-ab+b^2)$
The two directions are pretty distinct here. The one not intended simply confirms the equality by doing the straightforward multiplication and simplification that you showed. The intended direction is really to factor $a^3+b^3$, which is non-trivial. Confirming an identity is much easier than trying to discover a 'simpler' form like the RHS.
Feb
4
comment Where is $1 gone!
Word problems in secondary school math have this feel. The problem is like magic, misdirection by using words that are mostly correct but point away from a correct assessment of the reality.
Feb
4
comment Factorial and exponential dual identities
Yes, the second identity is a non-standard display of $\Gamma(n-1)$. That integral is usually chosen to be the definition of 'best' analytic continuation of $n!$. But really, in the above, $n$ is always an integer so there's no complication there.
Feb
4
comment Factorial and exponential dual identities
oops...yes...added.
Feb
4
revised Factorial and exponential dual identities
added dx
Feb
4
awarded  Student
Feb
4
asked Factorial and exponential dual identities
Feb
4
comment Striking applications of integration by parts
...which is dual to $\sum_{n\ge0} x^n/n! = e^x$.
Feb
4
comment How to know that $a^3+b^3 = (a+b)(a^2-ab+b^2)$
@Tom: The title of the question is different from what you ask in the contents. The title asks for how to know that they are equal. The contents take another direction and ask how to go from the LHS to the RHS. Douglas was most likely answering the title question, which is very reasonable.
Feb
4
comment algebra of Sets
Oh, reading the other answer I realize that, though my strategies are very general, there are specific strategies one can follow, and for proving set identities, one specific strategy is to show that every member of one side is a member of the other side (and vice versa).
Feb
4
comment algebra of Sets
Yes, because ...something about the A's and intersection. And then the nullset union another set is what?
Feb
4
comment what is some polynomial bound of the following expression?
Mathematica needs to work on its binomial simplification method. Is that $k(0 \choose k)$ for non-integer $k$?
Feb
2
answered algebra of Sets
Feb
1
revised Does a negative number really exist?
edited tags
Feb
1
answered Does a negative number really exist?
Feb
1
comment “Find $f '(a)$” explaining in english
Are you used to finding the tangent slope when the two points get really close? The quotient rule is easier than doing it from scratch (by calculating the limit), but if you don't have the quotient rule handy you can go through all the algebra with the limit. Do you know which method to find the derivative you're expected to use (quotient rule or limit or something else)?
Feb
1
comment Problems that are largely believed to be true, but are unresolved
@user3123 and Raphael: Here's the short reason - once you get past definitions (which hinder 'obviousness') it is 'obviously' true that $P \neq NP$ because there is an obvious exponential algorithm for SAT, and it's not obvious how to remove the 'trying every possibility' approach. There is doubt (we don't -know it's true) only because there is no proof (and proving a negative is hard), and there are other examples of where nondeterminism (-very- surprisingly) doesn't get you anything (language definiability in regular expressions and in TMs).