# Sherwiki

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Sherwiki at Wikia

Welcome to the Sherwiki mini wiki at Scratchpad!

You can use the box below to create new pages for this mini-wiki. Make sure you type [[Category:Sherwiki]] on the page before you save it to make it part of the Sherwiki wiki (preload can be enabled to automate this task, by clicking this link and saving that page. Afterwards, you may need to purge this page, if you still see this message).

## Some Set Inclusions

$\mathbb N\subset\mathbb Z\subset\mathbb Q\subset\mathbb R\subset\mathbb C$

## Limits of Sequences in $\mathbb R$

A sequence of real numbers, $(x_n)$, converges to $x\in\mathbb R$ if and only if for all $\epsilon>0$ there exists some $N\ge 1$ such that $|x_n-x|<\epsilon$ whenever $n\ge N$.

## Laplace Transforms

$F(s)=\int_0^\infty f(t)e^{-st}dt$

## Abelian Groups

A group, $(G,+)$, is abelian if and only if for all $g_1,g_2\in G$, $g_1+g_2=g_2+g_1$.