April 1, 2021May 7, 2021

Properties of the Supremum

The supremum and infimum of a bounded set of real numbers have many interesting properties

Study Help for Baby Rudin, Part 1.4

One of the properties of the supremum is that it is additive as a set function on sets of real numbers which are bounded above. — The supremum is additive as a set function on sets of real numbers which are bounded above.

The Completeness Axiom for the real number system is intimately tied to the concept of the supremum of a set of

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February 10, 2021February 10, 2021

Least Upper Bound (Supremum) in an Ordered Set

Suprema and Infima (Sups and Infs) Lie at the Heart of Real Analysis. The Range of Cos(n) is an Interesting Example.

Study Help for Baby Rudin, Part 1.3

For an ordered set $S$ and $M\subseteq S$ which is bounded above, the supremum of $M$ , when it exists in $S$ , is also called the least upper bound of $M$ in $S$ .

Which property separates the

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