Talk:Equivalence of Definitions of Real Exponential Function

If we want to keep $\exp x := e^x$ as a definition, then we have to clarify exactly what we're asserting. As it is, $e^x$ is defined as $\exp x \ln e$, which doesn't allow you to define \exp without being circular. Do we want to take the definition of integer and rational number indices and try to extend it to all real indices? Or scrap the def'n and just keep $e^x = \exp x \ln e$ as a justification of notation, rather than a definition? --GFauxPas 06:40, 8 February 2012 (EST)
 * They are now all interconnected except for the $e^x$ definition, which would be a nice, intellectually dishonest reason to scrap the $e^x$ definition. --GFauxPas 09:09, 8 February 2012 (EST)
 * Another suggestion: Keep the $\exp x = e^x$ as a definition for $x \in \Z, x \in \Q$, and prove the consistency for those. For $x \in \R \setminus \Q$, it will instead be a justification of notation. --GFauxPas 15:47, 9 February 2012 (EST)