test for your logic

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Krisi
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Re: test for your logic

Postby Krisi » Thu Feb 07, 2008 11:21 am

Xkalibur wrote:
krisi wrote:Xkalibur,
Do you want a numerical value to prove it?


No, there's no need for it. I'll show you how to do that in a logical way.


Answer.

A- is a rational number.
B- is an irrational number.
==============
A+B or A-B



1. Let's presume that sum A+B is a rational number:

A+B=C

C-> rational



2. If so, then B:

B=C-A would have been also rational as the difference of two rational numbers, but isn't so because it contradicts to the statement (B- an irrational number). Thus, our presumption was false and therefore sum A+B is an irrational number.


(A-B is similar to the above.)


Simple, isn't it? :)


Yes, yes. Got it! :)
Thanks.
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