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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 7505. If we assumed excluded middle, this would be essentially the same as ℕ_{∞} as defined at df-nninf 6770 but in its absence the relationship between the two is more complicated. (Contributed by AV, 10-Dec-2020.) |
Ref | Expression |
---|---|
df-xnn0 | ⊢ ℕ_{0}^{*} = (ℕ_{0} ∪ {+∞}) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cxnn0 8706 | . 2 class ℕ_{0}^{*} | |
2 | cn0 8643 | . . 3 class ℕ_{0} | |
3 | cpnf 7498 | . . . 4 class +∞ | |
4 | 3 | csn 3441 | . . 3 class {+∞} |
5 | 2, 4 | cun 2995 | . 2 class (ℕ_{0} ∪ {+∞}) |
6 | 1, 5 | wceq 1289 | 1 wff ℕ_{0}^{*} = (ℕ_{0} ∪ {+∞}) |
Colors of variables: wff set class |
This definition is referenced by: elxnn0 8708 nn0ssxnn0 8709 fxnn0nninf 9809 |
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