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| Mirrors > Home > MPE Home > Th. List > df-xnn0 | Structured version Visualization version GIF version | ||
| Description: Define the set of extended nonnegative integers that includes positive infinity. Analogue of the extension of the real numbers ℝ*, see df-xr 11299. (Contributed by AV, 10-Dec-2020.) |
| Ref | Expression |
|---|---|
| df-xnn0 | ⊢ ℕ0* = (ℕ0 ∪ {+∞}) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | cxnn0 12599 | . 2 class ℕ0* | |
| 2 | cn0 12526 | . . 3 class ℕ0 | |
| 3 | cpnf 11292 | . . . 4 class +∞ | |
| 4 | 3 | csn 4626 | . . 3 class {+∞} |
| 5 | 2, 4 | cun 3949 | . 2 class (ℕ0 ∪ {+∞}) |
| 6 | 1, 5 | wceq 1540 | 1 wff ℕ0* = (ℕ0 ∪ {+∞}) |
| Colors of variables: wff setvar class |
| This definition is referenced by: elxnn0 12601 nn0ssxnn0 12602 hashfxnn0 14376 hashf 14377 |
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