Definition df-xr 10997

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 10992	. 2 class ℝ*
2		cr 10854	. . 3 class ℝ
3		cpnf 10990	. . . 4 class +∞
4		cmnf 10991	. . . 4 class -∞
5	3, 4	cpr 4568	. . 3 class {+∞, -∞}
6	2, 5	cun 3889	. 2 class (ℝ ∪ {+∞, -∞})
7	1, 6	wceq 1541	1 wff ℝ* = (ℝ ∪ {+∞, -∞})

This definition is referenced by:  ressxr  11003  pnfxr  11013  mnfxr  11016  ltrelxr  11020  ssxr  11028  xrex  12709  elxr  12834  climxlim2lem  43340