\exists a,b,c \in \mathbb{R}; a+(b\cdot c)=(a+b)\cdot (a+c)

\exists b \in \mathbb{R} \forall a \in \mathbb{R}; a>b

\forall a \in \mathbb{R} \exists b \in \mathbb{R}; a>b

\exists a \in \mathbb{R} \exists b \in \mathbb{R}; a>b

\forall a \in \mathbb{R} \forall b \in \mathbb{R}; a>b

It is the minimum of the set of lower bounds of A

It is the supremum of the set of upper bounds of A

It is the maximum of the set of upper bounds of A

It is a lower bound

It always exists in \mathbb{Z} if A is a non empty subset of  \mathbb{Z} which is bounded below.

It is equal to -\sup(-A) where -A=\{-x | x\in A\}

It is the infimum of the set of lower bounds of A

It always exists in \mathbb{R}

It is equal to \min A