Any help would be greatly appreciated.
Let $m,n,p,q \in \mathbb{Z}$.
If $0 < m < n$ and $0 < p < q$ then $mp < nq$.
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@Ishfaaq m>n means m-n$\in$ $\mathbb{N}$. – user3182252 Feb 19 '14 at 03:55
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1see this: $mp<np\leq nq$ – Hesky Cee Feb 19 '14 at 03:57
2 Answers
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Given: $0 < m < n$
Multiply both sides by positive number p
=>$0 < mp < np$
Given: $0 < p < q$ so clear:
=>$0 < mp < np < nq$
=> $mp < nq$ as required.
QED
user223097
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$$ nq - mp = nq -np +np - mp = n(q-p) + (n-m)p $$ OR $$ nq - mp = nq -mq +mq - mp = (n-m)q + m(q-p) $$
Will Jagy
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@user3182252 My favorite high school teacher called it a Propitious Zero. Add and subtract the same thing. Sometimes it helps. – Will Jagy Feb 19 '14 at 04:09
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My professor has not taught or mentioned that, so I don't believe I can use that for this proof. – user3182252 Feb 19 '14 at 04:39
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@user3182252, when you get the chance, ask your professor or TA about the idea. – Will Jagy Feb 19 '14 at 05:03