answersLogoWhite

0


Best Answer

Yes, and for any non-zero rational x, the multiplicative inverse is 1/x.

User Avatar

Wiki User

โˆ™ 2017-02-26 20:49:04
This answer is:
User Avatar
Study guides

hio

โžก๏ธ
See all cards
3.11
โ˜†โ˜…โ˜†โ˜…โ˜†โ˜…โ˜†โ˜…โ˜†โ˜…
177 Reviews

Add your answer:

Earn +20 pts
Q: Does the set of rational numbers have a multiplicative inverse?
Write your answer...
Submit
Still have questions?
magnify glass
imp
Related questions

Is the set of rational numbers contains the multiplicative inverse of each of its members?

help me


What are the elements in rational numbers having multiplicative inverse?

All rational numbers, with the exception of zero (0), have a multiplicative inverse. In fact, all real numbers (again, except for zero) have multiplicative inverses, though the inverses of irrational numbers are themselves irrational. Even imaginary numbers have multiplicative inverses (the multiplicative inverse of 5i is -0.2i - as you can see the inverse itself is also imaginary). Even complex numbers (the sum of an imaginary number and a real number) have multiplicative inverses (the inverse of [5i + 2] is [-5i/29 + 2/29] - similar to irrational and imaginary numbers, the inverse of a complex number is itself complex). The onlynumber, in any set of numbers, that does not have a multiplicative inverse is zero.


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 number has no multiple inverse?

On the set of all real numbers ZERO has no multiplicative inverse. For other sets there may be other numbers too, so please define your set!


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.


What is the multiplicative identity of 2?

The multiplicative identity is a property of a set of numbers, not of an individual number in the set. 1 is the multiplicative identity for the set of all integers, rationals or reals etc. Individual elements of the set do have a multiplicative INVERSE and for 2, this is 1/2 or 0.5


Is the set of rational numbers contains the additive inverse of each of its members?

Yes.


What is the multiplicative inverse of ยฝ?

The multiplicative inverse of an element x (in a set S) is an element, y, of the set such that x*y = y*x = 1 where 1 is the multiplicative identity. y is denoted by x^(-1). For the set of numbers, the inverse of x is 1/x.


Does the set of rational numbers have an additive inverse?

No. It has a different additive inverses for each element.


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.


What is the difference between multiplicative inverse and additive inverse?

The multiplicative inverse of a non-zero element, x, in a set, is an element, y, from the set such that x*y = y*x equals the multiplicative identity. The latter is usually denoted by 1 or I and the inverse of x is usually denoted by x-1 or 1/x. y need not be different from x. For example, the multiplicative inverse of 1 is 1, that of -1 is -1.The additive inverse of an element, p, in a set, is an element, q, from the set such that p+q = q+p equals the additive identity. The latter is usually denoted by 0 and the additive inverse of p is denoted by -p.

People also asked