Definition df-pi 16023

Description: Define the constant pi, π = 3.14159..., which is the smallest positive number whose sine is zero. Definition of π in [Gleason] p. 311. (Contributed by Paul Chapman, 23-Jan-2008.) (Revised by AV, 14-Sep-2020.)

Assertion

Ref	Expression
df-pi	⊢ π = inf((ℝ+ ∩ (◡sin “ {0})), ℝ, < )

Detailed syntax breakdown of Definition df-pi

Step	Hyp	Ref	Expression
1		cpi 16017	. 2 class π
2		crp 12981	. . . 4 class ℝ+
3		csin 16014	. . . . . 6 class sin
4	3	ccnv 5675	. . . . 5 class ◡sin
5		cc0 11116	. . . . . 6 class 0
6	5	csn 4628	. . . . 5 class {0}
7	4, 6	cima 5679	. . . 4 class (◡sin “ {0})
8	2, 7	cin 3947	. . 3 class (ℝ+ ∩ (◡sin “ {0}))
9		cr 11115	. . 3 class ℝ
10		clt 11255	. . 3 class <
11	8, 9, 10	cinf 9442	. 2 class inf((ℝ+ ∩ (◡sin “ {0})), ℝ, < )
12	1, 11	wceq 1540	1 wff π = inf((ℝ+ ∩ (◡sin “ {0})), ℝ, < )

This definition is referenced by:  pilem2  26304  pilem3  26305