Definition df-xr 8153

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 8148	. 2 class ℝ*
2		cr 7966	. . 3 class ℝ
3		cpnf 8146	. . . 4 class +∞
4		cmnf 8147	. . . 4 class -∞
5	3, 4	cpr 3647	. . 3 class {+∞, -∞}
6	2, 5	cun 3175	. 2 class (ℝ ∪ {+∞, -∞})
7	1, 6	wceq 1375	1 wff ℝ* = (ℝ ∪ {+∞, -∞})

This definition is referenced by:  ressxr  8158  pnfxr  8167  mnfxr  8171  ltrelxr  8175  elxr  9940  xrex  10020