![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > df-xr | Structured version Visualization version GIF version |
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.) |
Ref | Expression |
---|---|
df-xr | ⊢ ℝ* = (ℝ ∪ {+∞, -∞}) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cxr 11245 | . 2 class ℝ* | |
2 | cr 11106 | . . 3 class ℝ | |
3 | cpnf 11243 | . . . 4 class +∞ | |
4 | cmnf 11244 | . . . 4 class -∞ | |
5 | 3, 4 | cpr 4623 | . . 3 class {+∞, -∞} |
6 | 2, 5 | cun 3939 | . 2 class (ℝ ∪ {+∞, -∞}) |
7 | 1, 6 | wceq 1533 | 1 wff ℝ* = (ℝ ∪ {+∞, -∞}) |
Colors of variables: wff setvar class |
This definition is referenced by: ressxr 11256 pnfxr 11266 mnfxr 11269 ltrelxr 11273 ssxr 11281 xrex 12969 elxr 13094 climxlim2lem 45071 |
Copyright terms: Public domain | W3C validator |