Definition:Bounded Ordered Set/Real Numbers/Definition 2

This page is about Bounded Subset of Real Numbers. For other uses, see Bounded.

Definition

Let $\R$ be the set of real numbers.

Let $T \subseteq \R$ be a subset of $\R$ such that:

$\exists K \in \R: \forall x \in T: \size x \le K$

where $\size x$ denotes the absolute value of $x$.

Then $T$ is bounded in $\R$.

Also see

• Equivalence of Definitions of Bounded Subset of Real Numbers

Sources

• 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 2$: Continuum Property: $\S 2.3$