Definition df-xr 10919

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 10914	. 2 class ℝ*
2		cr 10776	. . 3 class ℝ
3		cpnf 10912	. . . 4 class +∞
4		cmnf 10913	. . . 4 class -∞
5	3, 4	cpr 4560	. . 3 class {+∞, -∞}
6	2, 5	cun 3882	. 2 class (ℝ ∪ {+∞, -∞})
7	1, 6	wceq 1543	1 wff ℝ* = (ℝ ∪ {+∞, -∞})

This definition is referenced by:  ressxr  10925  pnfxr  10935  mnfxr  10938  ltrelxr  10942  ssxr  10950  xrex  12631  elxr  12756  climxlim2lem  43249