Show that the set of rational numbers is a field.
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If F is a field and if xy = 0 for x, y ∈ F, then x = 0 or y = 0. ... The set Q of rational numbers forms a field with respect to addition and multiplication. We can also define powers of rational numbers: if a ∈ Q is nonzero, we put a0 = 1 and an+1 = an · a.
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