test for your logic

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Vega
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test for your logic

Postby Vega » Tue Feb 05, 2008 12:47 pm

It is a simple little test. All you need to solve it- logical thinking.

A- is a rational number.
B- is an irrational number.

You must prove that the sum of A+B or the difference A-B is an irrational number.

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Re: test for your logic

Postby Krisi » Tue Feb 05, 2008 2:17 pm

Xkalibur wrote:It is a simple little test. All you need to solve it- logical thinking.

A- is a rational number.
B- is an irrational number.

You must prove that the sum of A+B or the difference A-B is an irrational number.


Difficult Xkalibur!
As I understood it, the sum of a whole number plus a non-terminating (not sure of term) decimal will be an irrational number. :)
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Re: test for your logic

Postby Vega » Tue Feb 05, 2008 2:36 pm

krisi wrote:Difficult Xkalibur!
As I understood it, the sum of a whole number plus a non-terminating (not sure of term) decimal will be an irrational number. :)


Yep.

Should I tell how to prove that or wait for some replies? I will tell you tomorrow. :wink:

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Re: test for your logic

Postby Krisi » Tue Feb 05, 2008 3:32 pm

Xkalibur wrote:
krisi wrote:Difficult Xkalibur!
As I understood it, the sum of a whole number plus a non-terminating (not sure of term) decimal will be an irrational number. :)


Yep.

Should I tell how to prove that or wait for some replies? I will tell you tomorrow. :wink:


I can wait Xkalibur. Yes, better to wait for some more replies.. :)
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Re: test for your logic

Postby denvinbo » Wed Feb 06, 2008 9:45 am

A hard test................
Hey! I'm stuck! Get me out!

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Re: test for your logic

Postby Vega » Wed Feb 06, 2008 1:44 pm

denvinbo wrote:A hard test................


Are you a schoolboy? What grade?

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Re: test for your logic

Postby denvinbo » Wed Feb 06, 2008 5:07 pm

9th.........
Hey! I'm stuck! Get me out!

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Re: test for your logic

Postby Krisi » Thu Feb 07, 2008 12:23 am

Xkalibur,
Do you want a numerical value to prove it?
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Re: test for your logic

Postby Krisi » Thu Feb 07, 2008 8:19 am

Xkalibur,
Please answer it now.
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Re: test for your logic

Postby Vega » Thu Feb 07, 2008 11:13 am

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? :)

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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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