All Questions

4 views

Equation, Area and Circumference of A circle given equation of the tangent and center

I don't know how to solve for the Area and Circumference but I know how to solve for the equation but I just wanted to make sure... Any help and explanations would be appreciated :) Problem: A circle ...
3 views

Concerning the problem of finding the number of invertible nxn random {1,0} matrcies

In a few more words, if we look at the space of all nxn matrices (over a field of characteristic 0) with only 1 or 0 as an element in them ("binary matrices"), how many of them are invertible for each ...
5 views

Applications of Infinitary Matrices in Set Theory

Matrices have a natural generalization to infinitary context. There are few known applications of such matrices in set theory. For example one may use Ulam matrices to show that real-valued measurable ...
11 views

How to prove that $\sup\{a_nb_n|n\in N\}\le \sup\{a_n|n\in N\}\sup\{b_n|n\in N\}$

It is known that $$a_n,\ b_n\ge0.$$ And they are both upper bounded. Knowing this how can one prove that $$\sup\{a_nb_n|n\in N\}\le \sup\{a_n|n\in N\}\sup\{b_n|n\in N\}$$ I don't see how to approach ...
6 views

How are these distributions called?

Are these any common distributions? Number of dependent trials until the first success occurs Inspired by (a) in this question here: Probability Problem with $n$ keys Binomial-like distribution ...
4 views

Relation between existense of a homomorphism and denseness of a set

Denote the pontryagin dual of a topolological group L by $\widehat L$. I encountered this claim for a discrete topological group $(G,\mathcal T)$ : Because there exists a one-to-one homomorphism ...
13 views

How to find trigonometry function limit

What is the solution for trigonometry functions limit when we're in $\dfrac{0}{0}$ situation? $$\lim_{x\to 0} \frac{\sin^2 3x}{x^2}$$ for example
7 views

Any ring of prime order commutative ?

Is any ring of prime order commutative ?
9 views

Number of disitinct subgroups of the automorphism group of the field of $3^{100}$ elements

Let $G$ be the group of all automorphisms of the field $F_{3^{100}}$ with $3^{100}$ elements . Then what is the number of distince subgroups of $G$ ? What is the order of $G$ ?
9 views

How is this topological space different from the euclidean one?

I'm preparing for my topology exam and came across this example which I can't figure out. Let $\mathcal{T}$ be a such family of all sets $U\subset \mathbb{R}^2$ that $U\cap L$ is an open set in L ...
6 views

Probability of getting the same 10 cards after a 110 card shuffle

Consider this situation: You have two standard decks merged together (104 cards). You give 10 cards to 4 players. What is the probability that the next time you deal (after the deck is randomly ...
13 views

Are $y_1$, $y_2$, $y_3$,

Let $v_1$, $v_2$, $v_3$, be linearly independent vectors in $\mathbb{R}^n$. Let $y_1$ = $v_2$-$v_1$, $y_2$ = $v_3$-$v_2$, $y_3$ = $v_3$-$v_1$. Are $y_1$, $y_2$, $y_3$ linearly dependent or ...
23 views

bounds of inregral: integral (from 0 to -pi)x^2*e^{-inx}dx=integral (from pi to 0)x^2*(e^{inx})dx

$$\int_{0}^{-\pi}x^2e^{-inx} \, \text{d}x = \int_{\pi}^0 x^2e^{inx} \, \text{d}x$$ which law allows such equality? why are they equal? I was thinking it is about putting $t=x-\pi$ but during my ...
8 views

Existence of weak Schauder-basis for concrete example.

Consider e. g. $P(X)$, the space of probability measures over some compact metrisable space, $X$. This may be viewed as a WOT*-compact subspace of some dual Banach space ...
9 views

A different characterization of the infimum of a set

Let $E$ be a set that is bounded below. Let $l$ be a lower bound of $E$. Show that $l = \inf E$ iff given any $\epsilon > 0$ we can always find $z \in E$ with $z < l + \epsilon$. Attempt ...
20 views

Prove, using Wronskian, that $e^\left(3x\right)$, $e^\left(2x\right)+x$, $e^\left(x\right)+1$ are linearly independent

I am currently working on a problem that asks to prove, using Wronskian, that $e^\left(3x\right)$, $e^\left(2x\right)+x$, $e^\left(x\right)+1$ are linearly independent. I went through the general ...
11 views

Show that an infinite set $C$ is equipotent to its cartesian product $C\times C$

So, as the title says I'd like to give a proof of the fact that if $C$ is an infinite set then it is equipotent or equivalent to its cartesian product $C\times C$ using Zorn's Lemma (and of course ...
24 views

empty boxes puzzle

The problem is N large empty boxes (assume they are of type:1) are initially placed on a table. An unknown number of boxes (type:1) are selected and in each of them K smaller boxes (type:2) are ...
14 views

Given the center of an elipse and three of its points, is this elipse completely determined? What is the easiest way to show that five points of an elipse are enough to determine the elipse?