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Mirrors > Home > ILE Home > Th. List > df-xnn0 | Unicode version |
Description: Define the set of extended nonnegative integers that includes positive infinity. Analogue of the extension of the real numbers , see df-xr 7470. If we assumed excluded middle, this would be essentially the same as ℕ_{∞} as defined at df-nninf 6735 but in its absence the relationship between the two is more complicated. (Contributed by AV, 10-Dec-2020.) |
Ref | Expression |
---|---|
df-xnn0 | NN0* |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cxnn0 8669 | . 2 NN0* | |
2 | cn0 8606 | . . 3 | |
3 | cpnf 7463 | . . . 4 | |
4 | 3 | csn 3431 | . . 3 |
5 | 2, 4 | cun 2986 | . 2 |
6 | 1, 5 | wceq 1287 | 1 NN0* |
Colors of variables: wff set class |
This definition is referenced by: elxnn0 8671 nn0ssxnn0 8672 fxnn0nninf 9772 |
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