Is the result of a number multiplied by a positive integer always larger than the original number (counterexample)?

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degeneratecircle eNotes educator| Certified Educator

The positive integers are 1,2,3,... and so on. Is there ever a time when multiplying doesn't make a number bigger? Multiplying by 1 will always keep the original number the same, so a counterexample to the statement

"Multiplying a number by a positive integer always results in a bigger number."

is `3*1=3.` Since the type of number being multiplied by a positive integer isn't specified, another counterexample would be `pi*1=pi.`

You don't always have to multiply by 1, though. A third counterexample is `0*100=0.`

If you want the result to be less than the original number, start with a negative number. For example, `-2*2=-4`, and `-4` is less than `-2`.

Something to take away from this is that multiplying by 1 or 0, or adding 0, represent special cases and can provide counterexamples.