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description:Exercises, tutorials, links, resources and theorem about mathematics from high-school to university level. How to guides, links and tutorials about GNU/Linux and Open source in general.

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Steinhaus theorem

Submitted by yonatan zilpa on Thu, 11/24/2016 - 13:15

Let $\lambda$ be Borel measure.If $A$ is mesuarable and $\lambda(A)>0$, then $A-A=\left\{ x-y\; :\; x,y\in A \right\}$ contains a segment $I$ such that $0\in I$ If $A, B$ are measurable sets and $\lambda(A), \lambda(B)>0$, then $A+B$ contains a segment I.Tags:theorems Read more about Steinhaus theorem1395 commentsLog in or register to post comments

Asymptotic Differentiable Function

Submitted by yonatan zilpa on Thu, 11/24/2016 - 14:45

Let $f$ be any function asymptotic at zero. Prove/Disprove:
If $f$ is differentiable everywhere in its domain, then $\lim_{x\to \infty}f\;'(x)$ must be equal to zero?Tags:recreational mathematics Read more about Asymptotic Differentiable Function1437 commentsLog in or register to post comments

Getting help in Tex Typesetting System

Submitted by yonatan zilpa on Wed, 05/15/2019 - 04:36

Normally Tex typesetting system distribution (such as TexLive, MikTex or TeTex) comes with a builtin help commands that provides excellent tutorials, books and plenty other documentations. Of course, the best way to learn it is to use it, so let's play with commands:Tags:texdoclaTextexTexLiveMikTex Read more about Getting help in Tex Typesetting System 1398 commentsLog in or register to post comments

Hahn Decomposition Theorem

Submitted by yonatan zilpa on Thu, 11/24/2016 - 14:07

Let $\nu$ be a signed measure over measurable space $(X,\mathcal{M})$. Denote $\tilde{N}=\left\{ u\in \mathcal{M} \; :\; \mbox{$u$ is $\nu$-negative}\right\}$ and $\tilde{P}=\left\{ u\in \mathcal{M} \; :\; \mbox{$u$ is$\nu$-positive} \right\}$ $\exists N\in \tilde{N}\Big(\exists P \in \tilde{P}\Big( N\cap P=\emptyset \; \mbox{ and }\; N\cup P = X\Big)\Big)$ $\forall N,N^{'}\in \tilde{N}\Big(\forall P,P^{'}\in \tilde{P} \Big(N\sqcup P =N^{'}\sqcup P^{'}=X \; \Longrightarrow \nu( P\triangle \tilde{P})=\nu( N\triangle \tilde{N})=0\Big)\Big) $ Tags:theorems Read more about Hahn Decomposition Theorem1399 commentsLog in or register to post comments

Google search tips

Submitted by yonatan zilpa on Thu, 11/24/2016 - 14:40

Tips and tricks on Google search techniques.Tags:google Read more about Google search tips1379 commentsLog in or register to post comments

Learning tips

Submitted by yonatan zilpa on Sun, 12/04/2016 - 14:54

How to make the most of your learning time? Efficient learning and good usage of time may be key ingredients. Each student may have his own unique style of learning, but there exist patterns and strategies that can help everyone. Here is a list of links to good webinars and lectures note that may help you chose your own style of learning. Tags:learning tips Read more about Learning tips1428 commentsLog in or register to post comments

The circle of Apollonius

Submitted by yonatan zilpa on Fri, 02/26/2016 - 17:05

By definition, a circle is the locus of all points equidistant from a fixed center. However, the circle of Apollonius is defined differently. In the following post I will define and construct an Apollonian circle. Tags:geometry Read more about The circle of Apollonius1340 commentsLog in or register to post comments

Finding which package provides a command

Submitted by yonatan zilpa on Tue, 05/14/2019 - 00:46

Suppose a command is not available in the system and we need to install it. How do we find a suitable package that provide this command? In Debian or Ubuntu we can simply run the following commandTags:aptapt-fileDebianUbuntu Read more about Finding which package provides a command1337 commentsLog in or register to post comments

Conceptual Language and Learning

Submitted by yonatan zilpa on Mon, 12/26/2016 - 15:17

Normally when we learn human spoken language we translate words to our ownmother tongue language. But when we learn our mother tongue language we have nolanguage to translate new words. How do we understand mother tongue withouttranslating words? Is there some kind of conceptual language where we cantranslate mother tongue new words? And if so, can we use this conceptuallanguage to become better learner?

Tags:learning tips Read more about Conceptual Language and Learning1478 commentsLog in or register to post comments

Four bottles - Equidistant mouth problems

Submitted by yonatan zilpa on Sun, 04/17/2016 - 05:29

How to place four identical bottles in the plane such that the distance between each pair of mouths will be the same?Tags:math recriation Read more about Four bottles - Equidistant mouth problems1535 commentsLog in or register to post comments Pages12next ›last » Homeindex

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Exercises, tutorials, links, resources and theorem about mathematics from high-school to university level. How to guides, links and tutorials about GNU/Linux and Open source in general.

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