Does one is forced to conclude that 2X = X \ sqrt -LCB- 2 -RCB- if series a + b + c + d + ... = X ?
Prove that if A , B , C , and D are sets , then -LRB- A ∩ B -RRB- X -LRB- C ∩ D -RRB- = -LRB- A X C -RRB- ∩ -LRB- B X D -RRB- . Deduce that the cartesian multiplication of sets distributes over the operation of intersection , that is , that -LRB- A X B -RRB- X C = -LRB- AXC -RRB- ∩ -LRB- BXC -RRB- and AX -LRB- B ∩ C -RRB- = -LRB- AXB -RRB- ∩ -LRB- AXC -RRB- for all A , B , and C. ?