Definition df-tau 12417

Description: Define the circle constant tau, tau = 6.28318..., which is the smallest positive real number whose cosine is one. Various notations have been used or proposed for this number including tau, a three-legged variant of pi, or 2 pi. Note the difference between this constant tau and the formula variable ta. 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	|- tau = inf ( ( RR+ i^i ( `' cos " { 1 } ) ) , RR , < )

Detailed syntax breakdown of Definition df-tau

Step	Hyp	Ref	Expression
1		ctau 12416	. 2 class tau
2		crp 9949	. . . 4 class RR+
3		ccos 12286	. . . . . 6 class cos
4	3	ccnv 4730	. . . . 5 class `' cos
5		c1 8093	. . . . . 6 class 1
6	5	csn 3673	. . . . 5 class { 1 }
7	4, 6	cima 4734	. . . 4 class ( `' cos " { 1 } )
8	2, 7	cin 3200	. . 3 class ( RR+ i^i ( `' cos " { 1 } ) )
9		cr 8091	. . 3 class RR
10		clt 8273	. . 3 class <
11	8, 9, 10	cinf 7242	. 2 class inf ( ( RR+ i^i ( `' cos " { 1 } ) ) , RR , < )
12	1, 11	wceq 1398	1 wff tau = inf ( ( RR+ i^i ( `' cos " { 1 } ) ) , RR , < )

This definition is referenced by:  taupi  16806