Definition df-xr 10679

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 10674	. 2 class ℝ*
2		cr 10536	. . 3 class ℝ
3		cpnf 10672	. . . 4 class +∞
4		cmnf 10673	. . . 4 class -∞
5	3, 4	cpr 4569	. . 3 class {+∞, -∞}
6	2, 5	cun 3934	. 2 class (ℝ ∪ {+∞, -∞})
7	1, 6	wceq 1537	1 wff ℝ* = (ℝ ∪ {+∞, -∞})

This definition is referenced by:  ressxr  10685  pnfxr  10695  mnfxr  10698  ltrelxr  10702  ssxr  10710  xrex  12387  elxr  12512  climxlim2lem  42175