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Proposition: For all rationals x and y != 0 the quotient is defined:

forall x in Q, y in Q\{0}: x = (x/y)*y.

Proof: see lecture notes.

Proposition: Between any two rational numbers, there is another rational number:

forall x in Q, y in Q: x < y => exists z in Q: x < z < y.

Proof: Take x in Q and y in Q with x < y. Then x < (x+y)/2 < y.

Author: Wolfgang Schreiner
Last Modification: November 16, 1999

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