Number theory question
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Number theory question

[From: ] [author: ] [Date: 12-02-12] [Hit: ]
Subtract 3 from both sides giving pi = x - 3, which is algebraic, leading to the contradiction that pi is algebraic.You can do the same kind of thing for 3 - pi.......
hey guys,

I'm not 100% confident, but I believe I read that it has been proven that a binary operation of two transcendental numbers can never yield a rational number.

Has anyone heard of this? and if so, could you point me in the direction of some resources.

Thanks in Advance,

David

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You heard incorrectly. 3 + pi is transcendental and so is 3 - pi. (3 + pi) + (3 - pi) = 6, which is not transcendental.

It is easy to show that 3 + pi and 3 - pi are transcendental.
Suppose that 3 + pi = x where x is algebraic.
Subtract 3 from both sides giving pi = x - 3, which is algebraic, leading to the contradiction that pi is algebraic. You can do the same kind of thing for 3 - pi.
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