Elementary Functions

Elementary Theory and Philip Spain ()
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Philip Spain: University of Glasgow, Department of Mathematics

Chapter Chapter III in Elements of Mathematics Functions of a Real Variable, 2004, pp 91-162 from Springer

Abstract: Abstract We know that every continuous homomorphism of the additive group R into the multiplicative group R * of real numbers ≠ 0 is a function of the form x ↦ a x (called an exponential function) where a is a number > 0 (TG, V, p.11); it is an isomorphism of R onto the multiplicative group $$R_ + ^*$$ of numbers > 0 if a ≠ 1, and the inverse isomorphism from $$R_ + ^*$$ onto R is denoted by log a x and is called the logarithm to the base a.

Keywords: Elementary Function; Multiplicative Group; Galois Extension; Differential Calculus; Continuous Homomorphism (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-59315-4_4

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DOI: 10.1007/978-3-642-59315-4_4

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