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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 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 $0\div0\cdot0$?