Definition df-xnn0 8707

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.)

Assertion

Ref	Expression
df-xnn0	⊢ ℕ0* = (ℕ0 ∪ {+∞})

Detailed syntax breakdown of Definition df-xnn0

Step	Hyp	Ref	Expression
1		cxnn0 8706	. 2 class ℕ0*
2		cn0 8643	. . 3 class ℕ0
3		cpnf 7498	. . . 4 class +∞
4	3	csn 3441	. . 3 class {+∞}
5	2, 4	cun 2995	. 2 class (ℕ0 ∪ {+∞})
6	1, 5	wceq 1289	1 wff ℕ0* = (ℕ0 ∪ {+∞})

This definition is referenced by:  elxnn0  8708  nn0ssxnn0  8709  fxnn0nninf  9809