Definition:Bounded Ordered Set/Real Numbers/Definition 1
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This page is about Bounded Subset of Real Numbers. For other uses, see Bounded.
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 $\R$.
- 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