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Prove that the set of all real no is a group with respect of multiplication?
Wiki User
∙ 14y ago
There are four requirements that need to be satisfied:
A. Closure: For any two elements of the group, a and b, the operation a*b is also a member of the group.
B. Associativity: For any three members of the group, a*(b*c) = (a*b)*c
C. Identity: There exists an element in the group, called the identity and denoted by i, such that a*i = i*a for all a in the group. For real numbers with multiplication, this element is 1.
D. Inverse: For any member of the group, a, there exists a member of the group, b, such that a*b = b*a = 1 (the identity). b is called the inverse of a and denoted by a-1.
Wiki User
∙ 14y ago
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