Description: Definition of the extended integers. (Contributed by BJ, 28-Jul-2023)
Ref | Expression | ||
---|---|---|---|
Assertion | df-bj-zzbar | ⊢ ℤ̅ = ( ℤ ∪ { -∞ , +∞ } ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
0 | czzbar | ⊢ ℤ̅ | |
1 | cz | ⊢ ℤ | |
2 | cminfty | ⊢ -∞ | |
3 | cpinfty | ⊢ +∞ | |
4 | 2 3 | cpr | ⊢ { -∞ , +∞ } |
5 | 1 4 | cun | ⊢ ( ℤ ∪ { -∞ , +∞ } ) |
6 | 0 5 | wceq | ⊢ ℤ̅ = ( ℤ ∪ { -∞ , +∞ } ) |