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Formalization of mathematics

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Exponentiation

Exponential function

Definition of the exponential function

{c}

The <Taylor series> expansion is the most direct definition of the expontial as it obviously satisfies the <exponential function differential equation>:
* the first constant term dies
* each other term gets converted to the one before
* because we have <infinite> many terms, we get what we started with!
$$
e^x = \sum_{n=0}^\infty \frac{x^n}{n!} = 1 + \frac{x}{1} + \frac{x^2}{2} + \frac{x^3}{2 \times 3} + \frac{x^4}{2 \times 3 \times 4} + \ldots
$$


Taylor expansion definition of the exponential function

Exponential map

Taylor expansion definition of the exponential function

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Taylor expansion definition of the exponential function

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