After a small search that I did I was unable to spot any answers here.What I am trying is to prove why the 2^sprt{2} is transcendental number.I know that this probably is a closed problem and probably many people have proved it already,but I want to reach the answer by myself after doing a research on this problem and going through several books and sources and test my knowledge and my power.So what I basically need is to give me guideline to solve the problem.If my question is too general,before you close it,please give me some information to rephrase,so it won't be so general.
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closed as off topic by Charles, unknown (google), Victor Protsak, Henry Cohn, Todd Trimble Sep 24 at 18:27 |
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By the Gelfond–Schneider theorem, $2^{\sqrt2}$ is transcendental. $2^{\sqrt 2}$ is called the Gelfond–Schneider constant. See also http://math.stackexchange.com/questions/173804/deciding-whether-2-sqrt2-is-irrational-transcendental |
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Don't worry, your question is well-stated. Some of these simply stated questions about transcendental numbers are still unknown! I don't know about this one. But here is another: Is $\pi^\pi$ a rational number? This one was unknown 20 years ago, and I expect it is still unknown. |
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