User talk:MikeEnnen

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

$$\exists x_{1}, x_{2} \in \mathbb{A} : x_{1} \neq x_{2} \ \land \mathbb{A}\backslash \{x_{1}, x_{2}\} = \emptyset$$.

Example:

Notation:

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

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

$$\exists x_{1}, x_{2} \in \mathbb{Z} : x_{1} \neq x_{2} \ \land \ \mathbb{Z}\backslash \{x_{1}, x_{2}\} : y \neq x_{1} \ \land \ y \neq x_{2} : \forall p \in \mathfrak{P}  \ \ \forall x \in \mathbb{Z^*} \  x^2 = p \Rightarrow x_{1} = \sqrt{p} \in \mathbb{Z} \ \land \ x_{2} = -\sqrt{p} \in \mathbb{Z}$$

where $$x_{1}$$ and $$x_{2}$$ are the only 2 solutions in $$\mathbb{Z}$$ 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)