Definition df-xnn0 9313

Description: Define the set of extended nonnegative integers that includes positive infinity. Analogue of the extension of the real numbers ℝ^*, see df-xr 8065. If we assumed excluded middle, this would be essentially the same as ℕ_∞ as defined at df-nninf 7186 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 9312	. 2 class ℕ0*
2		cn0 9249	. . 3 class ℕ0
3		cpnf 8058	. . . 4 class +∞
4	3	csn 3622	. . 3 class {+∞}
5	2, 4	cun 3155	. 2 class (ℕ0 ∪ {+∞})
6	1, 5	wceq 1364	1 wff ℕ0* = (ℕ0 ∪ {+∞})

This definition is referenced by:  elxnn0  9314  nn0ssxnn0  9315  xnn0nnen  10529  fxnn0nninf  10531