Question

Bestimmen Sie, falls existent, Supremum und Infimum folgender Mengen:

a) A = { x ∈ Q | 1/x ∈ N }

b) B = { x ∈ Q | 1/x ∈ N } U {0}

c) C = { x ∈ Q | ∃ n ∈ N : x = 1/n + (-1) ⁿ }

d) D = { 3ⁿ/n | n ∈ N}

Answer 1

A = { x ∈ Q | 1/x ∈ N }
1/x = n ∈ N   <=>  x = 1/n  also inf = 0 und sup = max = 1.

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