Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 153

show that all trees are planar without using Euler's formula or the fact that all trees are planar

the question is this: Show that all trees are planar I thought about using Euler's formula to show this but then I was told that I wasn't allowed to assume...

Asked on 01/11/2021 by user812532

1 answer

Is cardinality of sigma-algebra for two independent random variables is the sum of cardinalities of two sigma-algebras?

Let's say that there are two independent r.v. $A$ and $B$. Is $card {sigma(A,B)}$ the sum of $card {sigma(A)}$ and $card {sigma(B)}$, where $card$...

Asked on 01/11/2021

0 answer

expectation of random probability measure

Given $mu(omega, B)$ is a random probability measure on $mathbb{R}_{geq 0}$. This means for each $B$, it is a random variable, and for each $omega$ it...

Asked on 01/11/2021 by Xiao

1 answer

How many solutions are there to $x_1 + x_2 + x_3 + x_4 = 30$ s.t. $x_1 + x_2 le 20$ and $x_3 ge 7$?

Here is the original question from the book:How many ways are there to distribute $30$ green balls to $4$ persons if Alice and Eve together get no more...

Asked on 01/11/2021 by Lucas Peres

1 answer

How to prove that this series of functions is uniformly convergent?

Let ${f_n}$ be a sequence of functions on $[a, b]$ such that:$f_n(x) le 0$ if $n$ is even, $f_n(x) ge 0$ if $n$...

Asked on 01/10/2021 by Applesauce44

1 answer

Proving that holomorphic map $f : mathbb{C}^n to mathbb{C}^m$ maps holomorphic tangent space at point $p$ to holomorphic tangent space at $f(p)$

I'm trying to to prove proposition 2.3.1 from Jiri Lebl's text on several complex variables here. So far I have tried writing the jacobian in terms of...

Asked on 01/10/2021 by EmptyVessel

0 answer

Let $X$ be a metric space without isolated points. Then the closure of a discrete set in $X$ is nowhere dense in $X$.

I am having some trouble with this question from Willard's General Topology (p.37). I found that this was asked previously 9 years ago (see link: In a metric space...

Asked on 01/10/2021 by TuringTester69

3 answer

Fundamental theorem of Riemannian Geometry question

Theorem:Let $(M,g)$ be a Riemannian Manifold. Then there exists a unique Riemannian connection on $M$.My concern is with the existence part. In particular, I am unsure as to...

Asked on 01/10/2021 by monoidaltransform

2 answer

If given two groups $G_1,G_2$ of order $m$ and $n$ respectively then the direct product $G_{1}times G_{2}$ has a subgroup of order $m$.

I'm trying to understand if this statement is false or true, I have tried understanding by an example. For example if $G_1=({{bar0},bar1},+_2),G_3=({{bar0},bar1,bar2},+_3)$ then the direct product of these two...

Asked on 01/10/2021 by user3133165

2 answer

Show that if ${s_{n_k}}_k$ converges to $L$, then ${s_n}_n$ converges to $L$.

Suppose a sequence ${s_n}_n$ is monotone increasing, consider any of its subsequences ${s_{n_k}}_k$. Show that if ${s_{n_k}}_k$ converges to $L$, then ${s_n}_n$ converges to ...

Asked on 01/10/2021 by xhsbm

0 answer

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