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Nonempty set of real numbers

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Reference no: EM131233572

Let A be a nonempty set of real numbers. Prove that A is bounded in the sense of 1.3.1 if and only if there exists a positive real number K such that |x|<=K for all x in A.

1.3.1 Let F be an ordered field. A nonempty subset A of F is said to be:

bounded above if there exists an element K in F such that x <=K for all x in A.

bounded below if there exists an element k in F such that k<=x for all x in A.

bounded if it is both bounded above and bounded below.

unbounded if it is not bounded.

Reference no: EM131233572

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