Definition df-xr 10366

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 10361	. 2 class ℝ*
2		cr 10223	. . 3 class ℝ
3		cpnf 10359	. . . 4 class +∞
4		cmnf 10360	. . . 4 class -∞
5	3, 4	cpr 4379	. . 3 class {+∞, -∞}
6	2, 5	cun 3774	. 2 class (ℝ ∪ {+∞, -∞})
7	1, 6	wceq 1637	1 wff ℝ* = (ℝ ∪ {+∞, -∞})

This definition is referenced by:  ressxr  10371  pnfxr  10380  mnfxr  10384  ltrelxr  10387  ssxr  10395  xrex  12046  elxr  12169  climxlim2lem  40552