Definition df-xr 7998

Description: Define the set of extended reals that includes plus and minus infinity. Definition 12-3.1 of [Gleason] p. 173. (Contributed by NM, 13-Oct-2005.)

Assertion

Ref	Expression
df-xr	⊢ ℝ* = (ℝ ∪ {+∞, -∞})

Detailed syntax breakdown of Definition df-xr

Step	Hyp	Ref	Expression
1		cxr 7993	. 2 class ℝ*
2		cr 7812	. . 3 class ℝ
3		cpnf 7991	. . . 4 class +∞
4		cmnf 7992	. . . 4 class -∞
5	3, 4	cpr 3595	. . 3 class {+∞, -∞}
6	2, 5	cun 3129	. 2 class (ℝ ∪ {+∞, -∞})
7	1, 6	wceq 1353	1 wff ℝ* = (ℝ ∪ {+∞, -∞})

This definition is referenced by:  ressxr  8003  pnfxr  8012  mnfxr  8016  ltrelxr  8020  elxr  9778  xrex  9858