I want to get acquainted with rigorous definition of real exponents via limits of rational exponents. Can you suggest an article or a chapter in some textbook with topic about this ? All the posts on stackexchange on this topic I read, don`t really dive into proofs. And I could not find something with all the proofs on the internet. Thanks in advance.
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2I think there are some problems in Spivak's book Calculus that take this approach to defining $b^x$. – littleO Sep 22 '18 at 09:54
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1check pages 258-259 of this book: http://math.kennesaw.edu/~jlewin/CUP/marielle.pdf – Sep 22 '18 at 11:36