- #1
feyomi
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If A = {(x,y) : x³ = y² = e, yx = xˉ¹y} and B = {(u,v) : u^4 = v² = e, vu = uˉ¹v}, how do I go about finding the orders of, say, (x,v) and (x,u²) in A x B?
Thanks.
Thanks.
In the context of mathematics, orders refer to the number of elements in a set or the size of a group. In the case of A x B, it represents the number of elements in the Cartesian product of two sets A and B.
The orders of A x B can be calculated by multiplying the orders of the two individual sets, A and B. So if A has m elements and B has n elements, the orders of A x B would be m x n.
(x,v) and (x,u²) refer to ordered pairs in the Cartesian product A x B. These ordered pairs are formed by taking one element from set A and one element from set B, and ordering them in a specific way. In (x,v), x is the first element and v is the second element, while in (x,u²), x is the first element and u² is the second element.
The orders of (x,v) and (x,u²) are the same in A x B, as they are both ordered pairs and therefore have the same number of elements. In general, the orders of all ordered pairs in A x B will be the same.
No, the orders of (x,v) and (x,u²) will always be the same in A x B. This is because ordered pairs are formed by taking one element from set A and one element from set B, and the number of elements in each set does not change. Therefore, the orders of (x,v) and (x,u²) will always be m x n, where m is the number of elements in set A and n is the number of elements in set B.