Definition df-tau 33164

Description: Define tau = 6.283185..., 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 variable ta which is a variable representing a propositional logic formula. Only the latter is italic, and 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 33163	. 2 class tau
2		crp 11832	. . . 4 class RR+
3		ccos 14795	. . . . . 6 class cos
4	3	ccnv 5113	. . . . 5 class `' cos
5		c1 9937	. . . . . 6 class 1
6	5	csn 4177	. . . . 5 class { 1 }
7	4, 6	cima 5117	. . . 4 class ( `' cos " { 1 } )
8	2, 7	cin 3573	. . 3 class ( RR+ i^i ( `' cos " { 1 } ) )
9		cr 9935	. . 3 class RR
10		clt 10074	. . 3 class <
11	8, 9, 10	cinf 8347	. 2 class inf ( ( RR+ i^i ( `' cos " { 1 } ) ) , RR , < )
12	1, 11	wceq 1483	1 wff tau = inf ( ( RR+ i^i ( `' cos " { 1 } ) ) , RR , < )

This definition is referenced by:  taupilem2  33168  taupi  33169