Discrete Math Find a counterexample for the statement.

Mathematics
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Find a counterexample for the statement.

For every real number N > 0, there is some real number x such that
Nx > x.

N =

Apr 20th, 2015

Nx > x is the same as (N - 1)x > 0.
If N > 1, then this is true for positive x.
If N < 1, then this is true for negative x.

The only variant remaining is N = 1. Then (N - 1)x always =0 and never >0.

So, the answer is N=1.

Apr 20th, 2015

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