Definition df-xr 8365

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 8360	. 2 class ℝ*
2		cr 8179	. . 3 class ℝ
3		cpnf 8358	. . . 4 class +∞
4		cmnf 8359	. . . 4 class -∞
5	3, 4	cpr 3710	. . 3 class {+∞, -∞}
6	2, 5	cun 3218	. 2 class (ℝ ∪ {+∞, -∞})
7	1, 6	wceq 1402	1 wff ℝ* = (ℝ ∪ {+∞, -∞})

This definition is used by:  ressxr  8370  pnfxr  8379  mnfxr  8383  ltrelxr  8387  elxr  10189  xrex  10269