Definition df-relog 13573

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.)

Assertion

Ref	Expression
df-relog	⊢ log = ◡(exp ↾ ℝ)

Detailed syntax breakdown of Definition df-relog

Step	Hyp	Ref	Expression
1		clog 13571	. 2 class log
2		ce 11605	. . . 4 class exp
3		cr 7773	. . . 4 class ℝ
4	2, 3	cres 4613	. . 3 class (exp ↾ ℝ)
5	4	ccnv 4610	. 2 class ◡(exp ↾ ℝ)
6	1, 5	wceq 1348	1 wff log = ◡(exp ↾ ℝ)

This definition is referenced by:  dfrelog  13575  reeflog  13578