$\exists x \in N, \forall y \in N, x \ge y$ $\exists x \in N, \forall y \in N, x \ge  y$
Why is this a false statement?
Intuitively, it seems that if you let x always equal y, then the statement always holds true.
 A: We have the statement: $\color{blue}{ \exists x \in N, \forall y \in N, x\geq y}$
This statements reads: There exists a natural number ($x$), that for all natural numbers ($y$), $x$ is greater than or equal to $y$.  
Which can be paraphrased as: There is one natural number which is greater than or equal to all of the natural numbers.
Or simply: There is a largest natural number.
Which is clearly false.

Contrast that to the statement: $\color{blue}{ \forall y \in N, \exists x \in N, x\geq y}$
Which reads: For all natural numbers there exists a natural number which is larger than or equal to it.
This statement is true.
Hence demonstrating that the order of the quantifiers makes has a significant impact as to the meaning of the statement.  They are not commutative.
A: The statement says that there is $x\in\Bbb N$, that when fixed, no matter what $y\in\Bbb N$ we pick, $x\geq y$.
If that was true, what happens when $y=x+1$?
A: Your proposition say that $\mathbb N$ is bounded. May be $$\exists x\in\mathbb N:\forall y\in\mathbb N, y\leq x$$
will make more sense (even if it's exactly the same thing, I'm usually ease with $\leq$ than $\geq$)
Then if $$\exists x\in\mathbb N: \forall y\in\mathbb N, y\leq x$$
you have to understand that there exists an element $x\in\mathbb N$ such that all natural numbers are in $[0,x]$ which is impossible because $\mathbb N$ is unbounded. Do you understand ? 
