## Google search tips

Submitted by yonatan zilpa on

Tips and tricks on Google search techniques.

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## Google search tips

Submitted by yonatan zilpa on

Tips and tricks on Google search techniques.- Read more about Google search tips
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## Hahn Decomposition Theorem

Submitted by yonatan zilpa on

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) $

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## The circle of Apollonius

Submitted by yonatan zilpa on

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.- Read more about The circle of Apollonius
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## Finding which package provides a command

Submitted by yonatan zilpa on

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 command- Read more about Finding which package provides a command
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## Asymptotic Differentiable Function

Submitted by yonatan zilpa on

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?- Read more about Asymptotic Differentiable Function
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## Learning tips

Submitted by yonatan zilpa on

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.- Read more about Learning tips
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## Steinhaus theorem

Submitted by yonatan zilpa on

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.

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## Four bottles - Equidistant mouth problems

Submitted by yonatan zilpa on

How to place four identical bottles in the plane such that the distance between each pair of mouths will be the same?- Read more about Four bottles - Equidistant mouth problems
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## Conceptual Language and Learning

Submitted by yonatan zilpa on

Normally when we learn human spoken language we translate words to our own mother tongue language. But when we learn our mother tongue language we have no language to translate new words. How do we understand mother tongue without translating words? Is there some kind of conceptual language where we can translate mother tongue new words? And if so, can we use this conceptual language to become better learner?- Read more about Conceptual Language and Learning
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## Getting help in Tex Typesetting System

Submitted by yonatan zilpa on

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:- Read more about Getting help in Tex Typesetting System
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