# The Axiom of Completeness for the real numbers says: Every set of real numbers that has an upper bound has a least upper bound that is a real number. (a) Show that the italicized statement is false if the word real is replaced by rational. (b) Would the italicized statement be true or false if the word real were replaced

The Axiom of Completeness for the real numbers says: Every set of real numbers that has an upper bound has a least upper bound that is a real number.

(a) Show that the italicized statement is false if the word real is replaced by rational.

(b) Would the italicized statement be true or false if the word real were replaced by natural?

(a) Show that the italicized statement is false if the word real is replaced by rational.

(b) Would the italicized statement be true or false if the word real were replaced by natural?

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