There is no greater real number.
There is no positive integer that is greater than any other positive integer.
I was wondering if the negative sign is necessary here or not. Are there many different ways of writing the two statements?
There is no greater real number.
There is no positive integer that is greater than any other positive integer.
I was wondering if the negative sign is necessary here or not. Are there many different ways of writing the two statements?
There are many ways of writing these statements using first order logic. As said by @JavaMan and @AndréNicolas, you can use the logical equivalence between the quantifiers.
There is no greater real number.
I assume that, as you're using "greater", there must be some number, lets say $n$, whom no real number can be greater than.
$G(x,y)$ means $x$ is greater than $y$. And assume $x,y,n \in \mathbb{R}$.
$\forall x ~\neg G(x,n)$ or $\neg \exists x ~G(x,n)$
There is no positive integer that is greater than any other positive integer.
$P(x)$ means $x$ is positive. In this case $x,y \in \mathbb{Z}$.
$\neg \exists x ~\forall y~P(x) \wedge G(x,y)$
I'll let you do the other ones.
Hope it was helpfull.