Definition:Bounded Mapping/Unbounded

Definition

Let $\struct {T, \preceq}$ be an ordered set.

Let $f: S \to T$ be a mapping.

$f$ is unbounded if and only if $f$ is not bounded.

That is, if and only if $f$ is either unbounded above or unbounded below, or both.

Also known as

An unbounded mapping is also known as an unbounded function.

Also see

• Results about unbounded mappings can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): unbounded function
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): unbounded function