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Definition df-xnn0 12597
Description: Define the set of extended nonnegative integers that includes positive infinity. Analogue of the extension of the real numbers *, see df-xr 11296. (Contributed by AV, 10-Dec-2020.)
Assertion
Ref Expression
df-xnn0 0* = (ℕ0 ∪ {+∞})

Detailed syntax breakdown of Definition df-xnn0
StepHypRef Expression
1 cxnn0 12596 . 2 class 0*
2 cn0 12523 . . 3 class 0
3 cpnf 11289 . . . 4 class +∞
43csn 4630 . . 3 class {+∞}
52, 4cun 3960 . 2 class (ℕ0 ∪ {+∞})
61, 5wceq 1536 1 wff 0* = (ℕ0 ∪ {+∞})
Colors of variables: wff setvar class
This definition is referenced by:  elxnn0  12598  nn0ssxnn0  12599  hashfxnn0  14372  hashf  14373
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