**β π΄π β 1 and β π΄π β 1 a) π΄π = {π, π + 1,π + 2, β¦ } b) π΄π = {0,π} c) π΄π = {βπ, β π + 1, β¦ , β1, 0, 1, β¦ , π β 1, π} d) π΄π = {βπ, π}**

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Let us findΒ $\bigcup\limits_{i=1}^{\infty} A_i$Β andΒ $\bigcap\limits_{i=1}^{\infty} A_i$Β for the following setsΒ $A_i.$

a) IfΒ $π΄_π = \{π, π + 1,π + 2, β¦ \}$Β thenΒ $\bigcup\limits_{i=1}^{\infty} A_i=A_1=\mathbb N$Β andΒ $\bigcap\limits_{i=1}^{\infty} A_i=\emptyset.$

b) ForΒ $π΄_π = \{0,π\}$Β we get thatΒ $\bigcup\limits_{i=1}^{\infty} A_i=\{0,1,2,...\}=\mathbb N_0$Β andΒ $\bigcap\limits_{i=1}^{\infty} A_i=\{0\}.$

c) IfΒ $π΄_π = \{βπ, β π + 1, β¦ , β1, 0, 1, β¦ , π β 1, π\}$Β thenΒ $\bigcup\limits_{i=1}^{\infty} A_i=\mathbb Z$Β andΒ $\bigcap\limits_{i=1}^{\infty} A_i=A_1=\{-1,0,1\}.$

d) ForΒ $π΄_π = \{βπ, π\}$Β we get thatΒ $\bigcup\limits_{i=1}^{\infty} A_i=\mathbb Z\setminus\{0\}$Β andΒ $\bigcap\limits_{i=1}^{\infty} A_i=\emptyset.$