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Does the set of rational numbers have multiplicative identity?
Yes. The multiplicative identity for the rational numbers is 1 (also can be written as 1/1).
Does the set of rational numbers have a multiplicative identity?
Yes, it is 1.
What is the definition of multiplicative inverse?
In a set S, the multiplicative inverse of a non-zero element x is an element of the set, y, such that x*y = y*x = i, the identity element of S. For the set of numbers, the multiplicative identity is 1 and the multiplicative identity is also denoted by 1/x or x^-1.
Is the set of rational numbers contains the additive inverse of each of its members?
Yes.
Is 7 pie a rational number why or why not?
Assuming that you mean pi, and not pie, it is not a rational number.The set of rational numbers is a field and this means that for every non-zero rational number, there exists a multiplicative inverse in the setand also, due to closure, the product of any two rational numbers is a rational number.Now suppose 7*pi were rational.7 is rational and so there is its multiplicative inverse, which is (1/7).(1/7) is also rational so (1/7)*(7*pi) is rationalBut by the associative property, this is (1/7*7)*pi = 1*pi = pi.But it has been proven that pi is irrational. Therefore the supposition must be wrong ie 7*pi is not rational.
