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Mirrors > Home > ILE Home > Th. List > df-relog | GIF version |
Description: Define the natural logarithm function. Defining the logarithm on complex numbers is similar to square root - there are ways to define it but they tend to make use of excluded middle. Therefore, we merely define logarithms on positive reals. See http://en.wikipedia.org/wiki/Natural_logarithm and https://en.wikipedia.org/wiki/Complex_logarithm. (Contributed by Jim Kingdon, 14-May-2024.) |
Ref | Expression |
---|---|
df-relog | ⊢ log = ◡(exp ↾ ℝ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | clog 13116 | . 2 class log | |
2 | ce 11516 | . . . 4 class exp | |
3 | cr 7710 | . . . 4 class ℝ | |
4 | 2, 3 | cres 4581 | . . 3 class (exp ↾ ℝ) |
5 | 4 | ccnv 4578 | . 2 class ◡(exp ↾ ℝ) |
6 | 1, 5 | wceq 1332 | 1 wff log = ◡(exp ↾ ℝ) |
Colors of variables: wff set class |
This definition is referenced by: dfrelog 13120 reeflog 13123 |
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