If C 1 , C 2 , C 3 , are sets such that C k C k 1 , k 1, 2, 3, , lim k C k is defined as the intersection C 1 C 2 C 3 Find lim k C k if (a) C k x 2 1 k x 2 , k 1, 2, 3, (b) C k x 2 x 2 1 k , k 1, 2, 3, (c) C k (x, y) 0 x 2 y 2 1 k , k 1, 2, 3, ...

a In part a limk Ck limn Cn Since Ck Cn for a ...

If C 1 , C 2 , C 3 , . . . are sets such that

Question:

If C₁, C₂, C₃, . . . are sets such that C_k ⊃ C_k+1, k = 1, 2, 3, . . ., lim_k→∞ C_k is defined as the intersection C₁ ∩ C₂ ∩ C₃ ∩ · · · . Find lim_k→∞ C_k if
(a) C_k = {x : 2 − 1/k < x ≤ 2}, k = 1, 2, 3, . . . .
(b) C_k = {x : 2 < x ≤ 2 + 1/k}, k = 1, 2, 3, . . . .
(c) C_k = {(x, y) : 0 ≤ x² + y² ≤ 1/k}, k = 1, 2, 3, . . . .