Category:Exponential on Real Numbers is Group Isomorphism

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This category contains pages concerning Exponential on Real Numbers is Group Isomorphism:


Let $\struct {\R, +}$ be the additive group of real numbers.

Let $\struct {\R_{> 0}, \times}$ be the multiplicative group of positive real numbers.


Let $\exp: \struct {\R, +} \to \struct {\R_{> 0}, \times}$ be the mapping:

$x \mapsto \map \exp x$

where $\exp$ is the exponential function.


Then $\exp$ is a group isomorphism.