We will first write the negation of the statement before finding the counterexample!!!!

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

Negation : There exists a real number N>0 such that for all real numbers x it is true that Nx <= x

and any N in (0,1] works

the negation *is* a counterexample, so proving the negation is finding at least one N

it is true that for all x, Nx > x for N inside (0,1]

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