Name: Andrew M.
If 'N' is an irrational number. Is '2N' rational or
If 'N' is irrational, then so is '2N'.
'N' is irrational. If '2N' were rational, then '2N' can be expressed as a
ratio of integers: 2N=i/j. By dividing both sides by 2, N=i/(2j). Since
'j' is an integer, so is 2j. That would mean i/(2j)=N is a ratio of
integers, a rational number. We already know N is not rational. As a
result, our original assumption that 2N is rational cannot be true: 2N is
Illinois Central College
Irrational. Here is why: N is irrational. Assume, 2*N is rational. This
means: R= 2*N=p/q where 'p' and 'q' are integers. But then R/2 = p/2q is
also rational. But R/2 = N would have to be rational, which contradicts the
stipulation that N is irrational. QED by contradiction.
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Update: June 2012