ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  df-xr GIF version

Definition df-xr 7772
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 7767 . 2 class *
2 cr 7587 . . 3 class
3 cpnf 7765 . . . 4 class +∞
4 cmnf 7766 . . . 4 class -∞
53, 4cpr 3498 . . 3 class {+∞, -∞}
62, 5cun 3039 . 2 class (ℝ ∪ {+∞, -∞})
71, 6wceq 1316 1 wff * = (ℝ ∪ {+∞, -∞})
Colors of variables: wff set class
This definition is referenced by:  ressxr  7777  pnfxr  7786  mnfxr  7790  ltrelxr  7793  elxr  9518  xrex  9594
  Copyright terms: Public domain W3C validator