Hey /sci/, Im trying to teach myself basic set theory and I have a question concerning Cartesian Products. From what I (think) I understand, given sets A and B, #A×B=(#A)(#B).
My question is this: say A={1,2,5} and B={1,3,5,9,15}. I derived A×B to be the set {(1,1),(1,3),(1,5,),(1,9),(1,15),(2,1),(2,3),(2,5),(2,9,)(2,15),(5,1),(5,3),(5,5),(5,9),(5,15)}. Are the elements (1,5) and (5,1) distinct elements, or are they repetitive?
If theyre repetitive then I count 14 elements. If theyre distinct, I count 15. The statement #A×B=(#A)(#B) seems to state that in this case #A×B=15, in which case it appears that (1,5) and (5,1) are distinct elements of the set A×B.
Can someone confirm or deny this? Pls no bully.
My question is this: say A={1,2,5} and B={1,3,5,9,15}. I derived A×B to be the set {(1,1),(1,3),(1,5,),(1,9),(1,15),(2,1),(2,3),(2,5),(2,9,)(2,15),(5,1),(5,3),(5,5),(5,9),(5,15)}. Are the elements (1,5) and (5,1) distinct elements, or are they repetitive?
If theyre repetitive then I count 14 elements. If theyre distinct, I count 15. The statement #A×B=(#A)(#B) seems to state that in this case #A×B=15, in which case it appears that (1,5) and (5,1) are distinct elements of the set A×B.
Can someone confirm or deny this? Pls no bully.
