I am working through Walter Rudin's PMA and noticed he does not provide a very precise definition of exponentials. He just states that for an integer $n>0$ $$b^n=b\cdot b \cdot ... \cdot b$$ But he omits the proofs of $b^{n+m}=b^n b^m$, etc. as well as a definition for what $b^x$ is for any real $x$ I have just read chapter 1 so am I missing out or is it true that he omits these definitions/proofs? Thanks in advance.
2026-03-30 20:43:01.1774903381
Definition of exponents $b^x$ (Rudin PMA)
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(Third Ed.)
See exercise 6 chapter 1 , and the section on the exponential and logarithmic functions in chapter 8.