Definition df-xr 11181

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 11176	. 2 class ℝ*
2		cr 11035	. . 3 class ℝ
3		cpnf 11174	. . . 4 class +∞
4		cmnf 11175	. . . 4 class -∞
5	3, 4	cpr 4564	. . 3 class {+∞, -∞}
6	2, 5	cun 3888	. 2 class (ℝ ∪ {+∞, -∞})
7	1, 6	wceq 1547	1 wff ℝ* = (ℝ ∪ {+∞, -∞})

This definition is referenced by:  ressxr  11187  pnfxr  11197  mnfxr  11200  ltrelxr  11204  ssxr  11213  xrex  12935  elxr  13065  climxlim2lem  46289