Is the set of irrational numbers closed under the operation of exponentiation? That is, for all irrational numbers a and b, is a^b irrational? Why?
Last edited by thamathkid1729; Sep 25th 2011 at 03:16 PM.
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i do not know if is rational, but if it is not, then certainly is.
Originally Posted by thamathkid1729 Is the set of irrational numbers closed under the operation of exponentiation? That is, for all irrational numbers a and b, is a^b irrational? Why? http://www.math.sc.edu/~filaseta/gra...h785Notes8.pdf
Consider . if is a rational number than is irrational. So here you have an example of an irrational number raised to an irrational number yielding a rational number result.
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