Question

Show that the set of rational numbers from zero to infinity forms a mathematical group.​

Answer 1

Answer:

No. To say that the non-zero rationals form a group under division would mean that you could form a group from them using the division operation as if it was the composition operation in the group. The rationals excluding zero form a group under multiplication but not under division because division is not associative. In other words there are non-zero rational numbers such that (a÷b)÷c≠a÷(b÷c) In fact this is true unless c=1 or c=−1 . Associativity of the composition operation is one of the required axioms for a group, so this failure invalidates it.