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For every real number, x, which is not zero, there exists a real number x' such that x * x' = x' * x = 1, the multiplicative identity.

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Q: What an multiplicative inverse property and real number?
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Why doesn't every real number have a multiplicative inverse?

The only real (or complex) number which does not have a multiplicative inverse is 0. There is nothing you can multiply by 0 to get 1.

Is it true that any real number has a multiplicative inverse?

No, it is not true.

What is the product of any nonzero real number and its multiplicative inverse?


What number does not have a multiplicative inverse?

A multiplicative inverse for 2 numbers exists if the 2 numbers are coprime, i.e. their greatest common divisor (or gcd) is 1. However, if your question refers to just a singular number, virtually all real numbers (with the exception of zero) have a multiplicative inverse.

Do real numbers have a multiplicative inverse?

All real numbers, except 0, have a multiplicative inverse. For any real x, (x not = 0), there exists a real number y such that x*y = 1. This y is denoted by 1/x.

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.

What is a multiplicative inverse of an imaginary number?

The same as for a real number: 1 divided by the number.For example, the multiplicative inverse (or reciprocal) of 2i is 1 / 2i = -(1/2)i.

How do you prove the multiplicative inverse of a real number is unique?

To prove the uniqueness of the multiplicative inverse of a real number, let's assume that there are two different multiplicative inverses, say a and b, for a given real number x. This means that a * x = b * x = 1. By multiplying both sides of the equations by the common factor x, we get a = b = 1/x, which proves that the multiplicative inverse is indeed unique.

Does every non-zero number have a multiplicative inverse?

Every non zero number has a multiplicative inverse, which is 1 divided by that number. This stands for both real and complex numbers. This can be proved by letting x=some non zero number. x*(1/x)=x/x=1, therefore the multiplicative inverse of x is 1/x.

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.

Which real number does not have a multiplicative inverse and why?

That number is zero. It has no inverse because there is no number that you can multiply by zero to get one; to put this another way; The equation 0x= 1 has no solution, bacause 0x = 0 for all real numbers x.

Why can't you divide 100 by zero?

Because zero has no multiplicative inverse (no real number multiplied by 0 produces 1).