What does it mean by a^b in real number system? How is it defined mathematically?
It is clear in case of exponent being an integer.
i.e., a real number a is multiplied b times where b belongs to Z
If b is a rational..say b=p/q, then a^b can be interpreted as a^(1/q) multiplied p times.
But how is it defined when b is irrational?
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vara
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1Related. – Cameron Buie Nov 30 '13 at 00:42
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@Cameron Buie: thanks for the link and the answer provided in the link. – vara Nov 30 '13 at 01:11
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@Stefan: i tried searching before posting the question to no avail. Probably wrong choice of key words. – vara Nov 30 '13 at 01:13
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@vara : no problem. Glad I could help. – Stefan Smith Nov 30 '13 at 02:08
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You use the density of rationals in $\Bbb R$.Find a sequence $x_n\to \sqrt 2$ and $x_n<\sqrt 2$ for every $n$. Same for a sequence $y_n\to \sqrt 2$ with $y_n>\sqrt 2$. Then ...?
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@vara it is a little trickier than what is written here .. research it some more – Betty Mock Nov 30 '13 at 03:15