Definition df-xnn0 9581

Description: Define the set of extended nonnegative integers that includes positive infinity. Analogue of the extension of the real numbers RR*, see df-xr 8328. If we assumed excluded middle, this would be essentially the same as ℕ_∞ as defined at df-nninf 7424 but in its absence the relationship between the two is more complicated. (Contributed by AV, 10-Dec-2020.)

Assertion

Ref	Expression
df-xnn0	|- NN0* = ( NN0 u. { +oo } )

Detailed syntax breakdown of Definition df-xnn0

Step	Hyp	Ref	Expression
1		cxnn0 9580	. 2 class NN0*
2		cn0 9513	. . 3 class NN0
3		cpnf 8321	. . . 4 class +oo
4	3	csn 3694	. . 3 class { +oo }
5	2, 4	cun 3212	. 2 class ( NN0 u. { +oo } )
6	1, 5	wceq 1398	1 wff NN0* = ( NN0 u. { +oo } )

This definition is referenced by:  elxnn0  9582  nn0ssxnn0  9583  xnn0nnen  10823  fxnn0nninf  10825