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

Definition df-xr 9630
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  |-  RR*  =  ( RR  u.  { +oo , -oo } )

Detailed syntax breakdown of Definition df-xr
StepHypRef Expression
1 cxr 9625 . 2  class  RR*
2 cr 9489 . . 3  class  RR
3 cpnf 9623 . . . 4  class +oo
4 cmnf 9624 . . . 4  class -oo
53, 4cpr 3943 . . 3  class  { +oo , -oo }
62, 5cun 3377 . 2  class  ( RR  u.  { +oo , -oo } )
71, 6wceq 1437 1  wff  RR*  =  ( RR  u.  { +oo , -oo } )
Colors of variables: wff setvar class
This definition is referenced by:  ressxr  9635  ltrelxr  9646  ssxr  9654  xrex  11250  pnfxr  11363  mnfxr  11365  elxr  11367
  Copyright terms: Public domain W3C validator