Solution to ⋃ 𝐴𝑖 ∝ 1 and β‹‚ 𝐴𝑖 ∞ 1 a) 𝐴𝑖 = {𝑖, 𝑖 + … - Sikademy
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Archangel Macsika

⋃ 𝐴𝑖 ∝ 1 and β‹‚ 𝐴𝑖 ∞ 1 a) 𝐴𝑖 = {𝑖, 𝑖 + 1,𝑖 + 2, … } b) 𝐴𝑖 = {0,𝑖} c) 𝐴𝑖 = {βˆ’π‘–, βˆ’ 𝑖 + 1, … , βˆ’1, 0, 1, … , 𝑖 βˆ’ 1, 𝑖} d) 𝐴𝑖 = {βˆ’π‘–, 𝑖}

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


a) If 𝐴_𝑖 = \{𝑖, 𝑖 + 1,𝑖 + 2, … \}Β thenΒ \bigcup\limits_{i=1}^{\infty} A_i=A_1=\mathbb NΒ andΒ \bigcap\limits_{i=1}^{\infty} A_i=\emptyset.


b) For 𝐴_𝑖 = \{0,𝑖\}Β we get thatΒ \bigcup\limits_{i=1}^{\infty} A_i=\{0,1,2,...\}=\mathbb N_0Β andΒ \bigcap\limits_{i=1}^{\infty} A_i=\{0\}.


c) If 𝐴_𝑖 = \{βˆ’π‘–, βˆ’ 𝑖 + 1, … , βˆ’1, 0, 1, … , 𝑖 βˆ’ 1, 𝑖\}Β thenΒ \bigcup\limits_{i=1}^{\infty} A_i=\mathbb ZΒ andΒ \bigcap\limits_{i=1}^{\infty} A_i=A_1=\{-1,0,1\}.


d) For 𝐴_𝑖 = \{βˆ’π‘–, 𝑖\}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.

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Question ID: mtid-5-stid-8-sqid-776-qpid-661