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Definition df-xnn0 8647
Description: Define the set of extended nonnegative integers that includes positive infinity. Analogue of the extension of the real numbers *, see df-xr 7447. If we assumed excluded middle, this would be essentially the same as as defined at df-nninf 6712 but in its absence the relationship between the two is more complicated. (Contributed by AV, 10-Dec-2020.)
Assertion
Ref Expression
df-xnn0 0* = (ℕ0 ∪ {+∞})

Detailed syntax breakdown of Definition df-xnn0
StepHypRef Expression
1 cxnn0 8646 . 2 class 0*
2 cn0 8583 . . 3 class 0
3 cpnf 7440 . . . 4 class +∞
43csn 3425 . . 3 class {+∞}
52, 4cun 2984 . 2 class (ℕ0 ∪ {+∞})
61, 5wceq 1287 1 wff 0* = (ℕ0 ∪ {+∞})
Colors of variables: wff set class
This definition is referenced by:  elxnn0  8648  nn0ssxnn0  8649  fxnn0nninf  9747
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