Definition df-tau 12568

Description: Define the circle constant tau, τ = 6.28318..., which is the smallest positive real number whose cosine is one. Various notations have been used or proposed for this number including τ, a three-legged variant of π, or 2π. Note the difference between this constant τ and the formula variable 𝜏. Following our convention, the constant is displayed in upright font while the variable is in italic font; furthermore, the colors are different. (Contributed by Jim Kingdon, 9-Apr-2018.) (Revised by AV, 1-Oct-2020.)

Assertion

Ref	Expression
df-tau	⊢ τ = inf((ℝ+ ∩ (◡cos “ {1})), ℝ, < )

Detailed syntax breakdown of Definition df-tau

Step	Hyp	Ref	Expression
1		ctau 12567	. 2 class τ
2		crp 10071	. . . 4 class ℝ+
3		ccos 12437	. . . . . 6 class cos
4	3	ccnv 4775	. . . . 5 class ◡cos
5		c1 8186	. . . . . 6 class 1
6	5	csn 3709	. . . . 5 class {1}
7	4, 6	cima 4779	. . . 4 class (◡cos “ {1})
8	2, 7	cin 3219	. . 3 class (ℝ+ ∩ (◡cos “ {1}))
9		cr 8184	. . 3 class ℝ
10		clt 8366	. . 3 class <
11	8, 9, 10	cinf 7329	. 2 class inf((ℝ+ ∩ (◡cos “ {1})), ℝ, < )
12	1, 11	wceq 1402	1 wff τ = inf((ℝ+ ∩ (◡cos “ {1})), ℝ, < )

This definition is used by:  taupi  17330