Find a counterexample for the statement.

Mathematics
Tutor: None Selected Time limit: 1 Day

May 4th, 2015

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

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

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

  3. and any N in (0,1] works

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

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

May 4th, 2015

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