As I know, something can have only one definition, but can have multiply ways to define it and properties. So which one is the real definition of the exponential function?

Aug 22, 2021 · Finding exponential function limit definition from definition of e Ask Question Asked 4 years, 5 months ago Modified 2 years, 10 months ago

Oct 27, 2024 · Limit through definition Ask Question Asked 1 year, 2 months ago Modified 1 year, 2 months ago

Aug 23, 2023 · For every real number $x$, we define the natural exponential function to be $e^ {x} = \exp (x)$. Where $\exp$ denotes the inverse function of $\ln$, and $e$ is a number such that $\ln (e) …

Nov 7, 2018 · The exponential function is the unique smooth group isomorphism from the additive group of reals to the multiplicative group of positive reals whose derivative at zero is one.

Oct 16, 2020 · 1 There is a standard definition of exponential order used in the theory of Laplace transforms, which is a hypothesis in various theorems about them.

Jun 22, 2015 · Prove limit converges in definition of e. e. Ask Question Asked 10 years, 7 months ago Modified 1 year, 1 month ago

Jan 3, 2023 · My question : (1) Do these definitions exhaust the ways the exponential function can be defined? (2) Are these definitions actually different at least conceptually ( though denoting in fact the …

So here's my proof, using only the definition of the exponential function and elementary properties of limits. We use the following definition of the exponential function:

Simply define the exponential function exp(x) = ∑∞i = 0 and all the usual properties of exp(x) and ln(x) follow quite easily, with no need for the FTC. This is particuarly nice because most of the interesting …