Let A be a non empty subset of \mathbb{R} which is bounded below. What is True about \inf A ?

Question

Let   A  be a non empty subset of   \mathbb{R}  which is bounded below. What is True about   \inf A ?

Accepted Answer

It is a lower bound

Accepted Answer

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

Accepted Answer

It always exists in   \mathbb{R}

Answer

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

Answer

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

Answer

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

Answer

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

Answer

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

Answer

It is equal to   \min A

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