Definition:Bounded Set/Real Numbers/Definition 1

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 both bounded below and bounded above in $\R$.

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

Also see

• Equivalence of Definitions of Bounded Subset of Real Numbers

• Results about bounded sets of real numbers can be found here.

Sources

• 1964: Walter Rudin: Principles of Mathematical Analysis (2nd ed.) ... (previous) ... (next): Chapter $1$: The Real and Complex Number Systems: Real Numbers: $1.33$. Definition
• 1975: Bert Mendelson: Introduction to Topology (3rd ed.) ... (previous) ... (next): Chapter $2$: Metric Spaces: $\S 5$: Limits: Definition $5.5$
• 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 2$: Continuum Property: $\S 2.2$: The Continuum Property