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 Yearling
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Apr
9
comment Prove that there exists a unique real number $x$ between $0$ and $1$ such that $x ^{3} + x^2 − 1 = 0$.
Drop the intermediate value theorem. Check Derivative and find areas of monotonicity.
Apr
3
comment Doubt regarding quadratic sieve
I see where you're trying to go... you mixed the solution to the equation with the equation itself. Yes, if $$x^2=5\ (mod\ p)$$ and you've found that 10104 solves the equation, then $$p-10104$$ solves the same equation. But none of them solve the equation $$x^2=-5\ (mod\ p)=p-5\ (mod\ p)$$
Apr
3
comment Doubt regarding quadratic sieve
exploringnumbertheory.wordpress.com/2013/10/15/…
Apr
3
comment Doubt regarding quadratic sieve
But $$p-5(mod\ p) = -5(mod\ p)$$
Apr
3
comment Doubt regarding quadratic sieve
Can't be. You have a mistake. -5 and 5 mod 99991 are different elements of the modular groups Z/99991Z. Since $$10104^2$$ is indeed $$5 (mod 99991)$$, the first equation is wrong.
Jan
27
comment Integration of a measurable function
You are correct.
Jan
27
comment Integration of a measurable function
$f$ is a function.
Nov
29
awarded  Yearling
Nov
29
comment Two matrix proofs
Can you write B in terms of A?
Sep
20
comment If the proposition ¬p→v is true, then ¬p∨(p→q) ? Please check my solution.
Just draw the truth table.
Aug
23
comment Is $A+nB$ invertible when $A$ is invertible?
A possible direction: For $C_n=A+nB$ to be invertible, you need it's columns to be linearily independent (they need to be a basis for $\mathbb{R}^3$). So, it's basically a problem in proving that you can't have all sets of rows of all $C_n$s all linearily dependent.
Aug
8
comment Area of a Random Polygon
en.wikipedia.org/wiki/Bertrand_paradox_%28probability%29 could help.
Aug
5
comment Range of function $g(x)=\frac{e^{f(x)}-e^{|f(x)|}}{e^{f(x)}+e^{|f(x)|}}$
Try multiplying by the denominator.
Aug
5
revised Why do complex roots come in pairs?
deleted 19 characters in body
Aug
5
answered Why do complex roots come in pairs?
Aug
5
comment Why do complex roots come in pairs?
This also works if you have complex coefficients, you know.
Aug
5
comment Clarification about the concept of number
It was not fringe. It was mainstream (until Aristotelian philosophy took over). Think about the idea of an oath - it is precisely the idea that a lie (wrong signifier) hurts your soul, when uttered in the right circumstances.
Aug
5
comment Clarification about the concept of number
The nice thing about it, is that medieval philosophy (after Plato) assumed that you do put yourself where you sign. And that, if I burn a document with your name on it, I am in fact hurting you. In fact, this view was rather prevalent. Ever heard of voodoo?
Aug
5
answered Clarification about the concept of number
Aug
2
answered What is $0\div0\cdot0$?