For all m,n,p which are elements of the Integers:
(i) If p > 0 and mp < np then m < n
(ii) If p < 0 and mp < np then n < m
(iii) If m <= n and 0 <= p then mp <= np
Any help with the above proofs would be appreciated!
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i divide both sides of mp < np by p, and we get m<n.
ii divide both sides of mp<np by p. Don't forget to switch the sign, since p is negative.
iii multiply both sides of m <= n by p.
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