Name: Andrew M.
Status: student
Age: N/A
Location: N/A
Country: N/A
Date: N/A

Question:
If 'N' is an irrational number. Is '2N' rational or
irrational? why?

Replies:
Andrew,
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
irrational.

Dr. Mellendorf
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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