Mulltiplication and division are inverse processes for the same numbers involved in the operation. If my answer is not correct wait please for the edition of this question by an expert.
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this question on pic
There is not much to prove there; opposite numbers, by which I take you mean "additive inverse", are defined so that their sum equals zero.
assume its not. make two cases show that the two cases are equal
Answer this question… Which term best describes a proof in which you assume the opposite of what you want to prove?
Assume that f:S->T is invertible with inverse g:T->S, then by definition of invertible mappings f*g=i(S) and g*f=i(T), which defines f as the inverse of g. So g is invertible.
Suppose p and q are inverses of a number x. where x is non-zero. Then, by definition, xp = 1 = xq therefore xp - xq = 0 and, by the distributive property of multiplication over subtraction, x*(p - q) = 0 Then, since x is non-zero, (p - q) = 0. That is, p = q. [If x = 0 then it does not have a multiplicative inverse.]
I think so. Copy and paste method could be used to prove this. But this is only my opinion.
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.
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I can give you an example and prove it: eg. take the rational no. 2......hence its additive inverse ie. its opposite no. will be -2 now lets add: =(2)+(-2) =2-2 =0 it means that the opposite no.s. get cancelled and give the answer 0 this is the same case for sum of a rational no. and its opposite no. to be ZERO
Yes, that's how it is done. Assuming the contrary should eventually lead you to some contradiction.
A multiplicative inverse (or reciprocal) is a number 1/x which when multiplied by x yields the multiplicative identity (1). 2.1 = 2 and 1/10 = 21/10 21/10 x 10/21 = 210/210 = 1