Definition df-xr 11182

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 11177	. 2 class ℝ*
2		cr 11037	. . 3 class ℝ
3		cpnf 11175	. . . 4 class +∞
4		cmnf 11176	. . . 4 class -∞
5	3, 4	cpr 4584	. . 3 class {+∞, -∞}
6	2, 5	cun 3901	. 2 class (ℝ ∪ {+∞, -∞})
7	1, 6	wceq 1542	1 wff ℝ* = (ℝ ∪ {+∞, -∞})

This definition is referenced by:  ressxr  11188  pnfxr  11198  mnfxr  11201  ltrelxr  11205  ssxr  11214  xrex  12912  elxr  13042  climxlim2lem  46192