Question

Prove that the set of Rational numbers is a field with respect to
addition and multiplication.

Answer 1

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. This defines an for all n ∈ N; if n is negative, we put an = 1/a−n.

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