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Let $X$ be a real closed field. Let us define a constructible hierarchy relative to $X$ is defined as follows. (This is slightly nonstandard terminology.). Let...
1Mathematics Asked on 2 years ago
Original question: Let A and B be two points lying on opposite sides of a given line l. Find all point(s) X on l such that |AX − BX| is...
1Mathematics Asked by Vibhu Kapadia on 2 years ago
So I'm trying to solve this problem (which has some physics elements but it's mostly a math problem, I think). Here it is:Consider the image below: ...
1Mathematics Asked on 2 years ago
How does $$left(1+frac{x}{j}right)^{-1}left(1+frac{1}{j}right)^x=1+frac{x(x-1)}{2j^2}+Oleft(frac{1}{j^3}right)$$my attempt: It looks like maybe the taylor series of the numerator at 1 times the geometric of the denominator: $(1-(frac{x}{j})+(frac{x}{j})^2dots)(1+(1+1/j)^x(ln(1+1/j))(x-1)$ which obviously isn't the...
1Mathematics Asked on 2 years ago
When we take distance from the line, we take $$ d = frac{ Ax_o + By_o + C}{ sqrt{A^2 +B^2}}$$ usually with a modulus on top, now my question...
4Mathematics Asked on 2 years ago
Find the coefficient of $x^{24}$ in the equation ${left( {1 - x} right)^{ - 1}}.{left( {1 - {x^2}} right)^{ - 1}}.{left( {1 - {x^3}} right)^{ - 1}}$ My...
3Mathematics Asked on 2 years ago
Typically, in taylor series, I see an expansion about $x=0$ for some function $f(x)$ that we're approximating. I always thought this was just done for simplicity since this...
1Mathematics Asked on 2 years ago
How to check if $phi(n)$ is a perfect square?Here, $phi$ is Euler's totient function. That is,$phi(n)$ counts the positive integers up to a given integer ...
0Mathematics Asked by ppSpp on 2 years ago
$Q)$ Let the $S_n$ be the number of the positive roots $(x,y,z)$ of the $x+2y+3z=n$, $n geq 6$ (I.e. $x>0, y>0$ and ...
0Mathematics Asked on 2 years ago
This question is vaguely related to this MO question of mine. Suppose $V$ is a (for simplicity, well-founded) model of $mathsf{ZF+AD}$. Let $mathbb{P}$ be a forcing...
0Mathematics Asked on 2 years ago
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