User talk:MikeEnnen

"There exists exactly two things in an (arbitrary) set":

$\mathrm{\exists }{x}_1,x_2\in \mathbb{𝔸}:x_1\ne x_2\wedge \mathbb{𝔸}\mathrm{\setminus }\{x_1,x_2\}=\mathrm{\varnothing }$.

Example:

Notation:

Let ${\mathbb{\mathbb{Z}}}^{\mathbb{*}}=\{x\in \mathbb{\mathbb{Z}}:x>=0\}$. That is, ${\mathbb{\mathbb{Z}}}^{\mathbb{*}}$ is the set of all non-negative integers.

Let $\mathfrak{𝔓}=\{x^2:x\in \mathbb{\mathbb{Z}}\}$ denote the set of all perfect squares.

$\mathrm{\exists }{x}_1,x_2\in \mathbb{\mathbb{Z}}:x_1\ne x_2\wedge \mathbb{\mathbb{Z}}\mathrm{\setminus }\{x_1,x_2\}:y\ne x_1\wedge y\ne x_2:\mathrm{\forall }p\in \mathfrak{𝔓}\mathrm{\forall }x\in {\mathbb{\mathbb{Z}}}^{\mathbb{*}}{x}^2=p\Rightarrow x_1=\sqrt{p}\in \mathbb{\mathbb{Z}}\wedge x_2=-\sqrt{p}\in \mathbb{\mathbb{Z}}$ 

where $x_1$ and $x_2$ are the only 2 solutions in $\mathbb{\mathbb{Z}}$ to $x^2=p$, where $p\in \mathfrak{𝔓}$.

I realize this may not be the best example...tell me what ya'll think!

MikeEnnen (talk) 12:07, 28 May 2011 (UTC)

Looking back I have no idea what I was doing here.

MikeEnnen (talk) 19:10, 14 September 2011 (UTC)