Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 150

Dependence of coin tosses

We are tossing a coin $m$ times The probability of heads $Bbb P(H)$ is anywhere in $(0,1)$. It doesn't have to be a fair coin basically. Random...

Asked on 01/15/2021

1 answer

Is $z$ a point on the line $[x,y]={tx+(1-t)y: tin[0,1]}$?

In a normed space $M$ with $x,y,zin M$, i need show if this statement is true or false. $|x-y |= |x-z | + |z-y |$ if...

Asked on 01/15/2021 by Luis Prado

1 answer

Does $n$ divide $2^{n-1} - 1$ for an infinite number of composite $n$?

Yes, $p$ always divides $2^{p-1}-1$ for any prime $p ge 3$. Are there any odd composite $n$ for which $n$ divides $2^{n-1}-1$? And on...

Asked on 01/14/2021

1 answer

Entire function can be approximated uniformly by polynomials with rational coefficients on every compact set.

I am working on Stein Complex Analysis Chapter 2 Problem 5. The question has a hint that I cannot prove. Basically, the hint states as follows:Let $p_{1}, p_{2},cdots$ denote...

Asked on 01/14/2021 by JacobsonRadical

1 answer

Find a limit involving floor function

I had to find the following limit: $displaystyle{lim_{x to infty}}frac{x}{lfloor x rfloor}$ Where $xinmathbb{R}$ and $f(x)= {lfloor x rfloor}$ denotes the floor function. This is what I...

Asked on 01/14/2021

3 answer

Extending a morphism on stalks by base change

This question is from Qing Liu Algebraic Geometry and Arithmetic Curves chapter 3 exercise 2.5 on pg. 96. I've approached this is the same spirit as the answer given to...

Asked on 01/14/2021

0 answer

If $text{Mod}_{R}$ and $text{Mod}_{S}$ are equivalent, then $R$ and $S$ have the same simple modules.

Let $R$ and $S$ be (unital, associative) rings. If $text{Mod}_{R}$ and $text{Mod}_{S}$ are equivalent categories, then is it true that $R$ and $S$ have...

Asked on 01/14/2021

1 answer

How to evaluate the integral of the exponential of tangent squared?

I was stopped during evaluation of other problem by the integral of$$int_0^frac pi 2 e^{ictan^2theta}dtheta$$ where $cneq 0$ and $cinRe$.By variable substitution $x=tantheta$, it...

Asked on 01/14/2021 by MathArt

1 answer

Solution check: Uniform continuity

While reading Bartle's book, i came across the following: Problem: Prove that if $f$ is uniformly continuous on a bounded subset $A$ of $mathbb{R},$ then $f$...

Asked on 01/14/2021

1 answer

Algebraic closure of $mathbb F_p$

I'm proving that $overline{mathbb{F}}_p = bigcuplimits_{i=1}^{infty} mathbb{F}_{p^i}$ is an algebraic closure of $mathbb{F}_p$ where $p$ is a prime. I think I've gotten down how to prove that...

Asked on 01/14/2021 by SamoGrecco

1 answer

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