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Mirrors > Home > ILE Home > Th. List > df-xnn0 | 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 7995. If we assumed excluded middle, this would be essentially the same as ℕ∞ as defined at df-nninf 7118 but in its absence the relationship between the two is more complicated. (Contributed by AV, 10-Dec-2020.) |
Ref | Expression |
---|---|
df-xnn0 | ⊢ ℕ0* = (ℕ0 ∪ {+∞}) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cxnn0 9238 | . 2 class ℕ0* | |
2 | cn0 9175 | . . 3 class ℕ0 | |
3 | cpnf 7988 | . . . 4 class +∞ | |
4 | 3 | csn 3592 | . . 3 class {+∞} |
5 | 2, 4 | cun 3127 | . 2 class (ℕ0 ∪ {+∞}) |
6 | 1, 5 | wceq 1353 | 1 wff ℕ0* = (ℕ0 ∪ {+∞}) |
Colors of variables: wff set class |
This definition is referenced by: elxnn0 9240 nn0ssxnn0 9241 fxnn0nninf 10437 |
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