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Jul
28
asked Example of a well defined functional integral?
Jul
27
revised The existential theory is undecidable
edited tags
Jul
27
comment Substitution for limits
There really should be. But I think to make it more rigorous, will result in a lot of bad edge cases showing that the way go about doing certain limits, really is very loose.
Jul
27
answered Simplify Square Root Expression $\sqrt{125} - \sqrt{5}$
Jul
27
revised Simplify Square Root Expression $\sqrt{125} - \sqrt{5}$
edited tags
Jul
27
comment Substitution for limits
I pretty freely substitute as long as the f is an invertible function by the rule you have given above. When going to infinity, things get more ambiguous for example depending on what side (or in the complex plane what direction) one tends x to 0 $\frac{1}{x}$ gets a different value. Most of the times I've done that substitution, "stuff just works out at the end" I feel as though rigorous justification for that sort of trick, is very very specific to each problem it is being applied to. And that there should be plenty of cases out there, that show the 1/x substitution is ridiculous.
Jul
27
comment Proof of Cohn's Irreducibility Criterion
$$ a_0 + a_1 x + ... a_nx^n$$ where $ 0 \le a_i \le t$. And if it factors we assume it factors into $$b_0 + b_1x +... b_rx^r \times c_0 + c_1x + ... + c_jx^j$$ why should I believe that $0 \le b_i \le t$ and $0 \le c_i \le t$. That is not immediately clear to me.
Jul
27
comment Proof of Cohn's Irreducibility Criterion
Okay so you can divide out -1 from both factors (which cancels), so we only need to check a polynomial = 1. But that still doesn't fix the problem. We don't have any reason to believe that the polynomial factors themselves will be base t expansions. Meaning given that we wish to check
Jul
27
comment All natural numbers $m, n$ such that $m = \sqrt{\frac{1}3A^2 - 3n^2}$
Ah. It seems this problem was tackled by: scholarworks.boisestate.edu/cgi/…
Jul
27
answered All natural numbers $m, n$ such that $m = \sqrt{\frac{1}3A^2 - 3n^2}$
Jul
27
revised All natural numbers $m, n$ such that $m = \sqrt{\frac{1}3A^2 - 3n^2}$
edited tags
Jul
27
comment All natural numbers $m, n$ such that $m = \sqrt{\frac{1}3A^2 - 3n^2}$
Hello, weclome to math.se, in the future it is recommended you show your work on any problem you are asking a question for.
Jul
27
comment Proof of Cohn's Irreducibility Criterion
Why is it that the factors need to be expansions? I agree that the polynomial itself is a unique expansion, but how do I know that the factors themselves won't have negative terms and other funky business making -1 a possible factor
Jul
27
comment Proof of Cohn's Irreducibility Criterion
@AmerYR no worries, that post will still be helpful to others with the same question
Jul
27
comment Proof of Cohn's Irreducibility Criterion
@AmerYR It was shown that t need not be 10. As long as t is greater than all the coefficients and coefficients greater than 0. Your example has 2 negative numbers (not allowed). And needs to be evaluated for $t >26$
Jul
27
answered coefficient of $x^{17}$ in the expansion of $(1+x^5+x^7)^{20}$
Jul
27
comment Trending proof for fairly simple fraction
This is even more efficient than L'Hopitals!
Jul
27
comment Trending proof for fairly simple fraction
Welcome to the mystical world of Q Generalizations! (They are quite interesting to play with algebraically!)
Jul
27
asked Proof of Cohn's Irreducibility Criterion
Jul
26
accepted More Symmetric than the symmetric groups?