MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-xr Structured version   Visualization version   GIF version

Definition df-xr 11276
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 ∪ {+∞, -∞})

Detailed syntax breakdown of Definition df-xr
StepHypRef Expression
1 cxr 11271 . 2 class *
2 cr 11131 . . 3 class
3 cpnf 11269 . . . 4 class +∞
4 cmnf 11270 . . . 4 class -∞
53, 4cpr 4626 . . 3 class {+∞, -∞}
62, 5cun 3943 . 2 class (ℝ ∪ {+∞, -∞})
71, 6wceq 1534 1 wff * = (ℝ ∪ {+∞, -∞})
Colors of variables: wff setvar class
This definition is referenced by:  ressxr  11282  pnfxr  11292  mnfxr  11295  ltrelxr  11299  ssxr  11307  xrex  12995  elxr  13122  climxlim2lem  45227
  Copyright terms: Public domain W3C validator