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 ∪ { -∞ , +∞ } ) |