For each subset of real numbers find its supremum maximum in

For each subset of real numbers find its supremum, maximum, infinum, and minimum if it exists for A = {set of all irrational numbers excluding pi and root of 2. You must justify all your answers.

Solution

there is no supremum, maximum, infimum or minimum of A because A contains an infinity of elements which can be arbitrary small or arbitrary large (example: -n and n, where n is not a square)

For each subset of real numbers find its supremum, maximum, infinum, and minimum if it exists for A = {set of all irrational numbers excluding pi and root of 2.

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