Definition df-xr 11013

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 11008	. 2 class ℝ*
2		cr 10870	. . 3 class ℝ
3		cpnf 11006	. . . 4 class +∞
4		cmnf 11007	. . . 4 class -∞
5	3, 4	cpr 4563	. . 3 class {+∞, -∞}
6	2, 5	cun 3885	. 2 class (ℝ ∪ {+∞, -∞})
7	1, 6	wceq 1539	1 wff ℝ* = (ℝ ∪ {+∞, -∞})

This definition is referenced by:  ressxr  11019  pnfxr  11029  mnfxr  11032  ltrelxr  11036  ssxr  11044  xrex  12727  elxr  12852  climxlim2lem  43386