Hello guys!

First of all i would like to express my happiness of the forum coming back live. Nothing is better than this .

I'm not quite sure if anyone here has used Z to represent discrete mathematics here before. But this is the notation which i've been taught at the uni. But since i'm not having much of a help on this. I'm a bit feeling a bit left alone. I got to finish this assignment off I about week time.

Could anyone please help me point out some direction on where to start? Which inference rule to apply first to simplify the following quantification using one-point rule and predicate logic

$\displaystyle \exists x:\mathbb{N}\bullet(\forall y:\mathbb{N}\bullet y\neq z \vee y \neq x) \Rightarrow (\forall y:\mathbb{N} \bullet z > y)$

'z' is assumed to be an integer.

As you can see in the predicate part the implication holds. But i'm quite struggling to understand what $\displaystyle y \neq z)$ is actually represnting. 'z' can be an positive or a negative integer. If y is not equal to z meaning that y is always above 0 as its of type natual number.

thanks a lot guys

ssharish