Suppose m1 < m2 and n1 < n2. Show that m1n1 < m2n2.
ANy advice...THanks in advance.
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Hello jzellt Originally Posted by jzellt Suppose m1 < m2 and n1 < n2. Show that m1n1 < m2n2.
ANy advice...THanks in advance. Not true. 3<8 and -2<-1, but -6>-8.
Perhaps you meant to say that these are natural numbers? In which case, , for some , and for some .
Last edited by Grandad; February 13th 2009 at 04:23 AM.
Reason: Added proof of suggested amendment
A bit simpler, I think: If , and then . If and then . Those together ("<" is a transitive relation) give .
Notice that does not say anything about . This only requires that 3 of the four numbers be positive.
Last edited by HallsofIvy; February 13th 2009 at 08:48 AM.
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