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You can invert almost any number by dividing 1 by that number. Zero is an exception since division by zero yields the equivalent of infinity, which is difficult to deal with by the usual rules of arithmetic. We cannot really know what the product of zero and infinity is. All other real numbers can be inverted.

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โˆ™ 2012-11-22 15:52:21
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Q: Does every real number have a multiplicative inverse?
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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.

What an multiplicative inverse property and real number?

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.

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.

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

No, it is not true.

What is the difference between additive and multiplicative inverse?

The additive inverse is the inverse under addition; the multiplicative inverse is the inverse under multiplication. For example, the additive inverse of any real or complex number is its negative: the inverse of 3 is -3 and vice versa. The multiplicative inverse of a number other than 0 (which has no such inverse) is its reciprocal: the inverse of 2 is 1/2, and vice versa. Adding a number and its additive inverse gives the additive identity, 0. Multiplying a number by its multiplicative inverse gives the multiplicative identity, 1.

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


Does every real numbers have a multiplicative inverse?

No, zero does not. Multiplicative inverse, also known as reciprocal, is a number which multiplied by the original number gives 1 for the answer. Zero, multiplied by any numberequals zero. Infinity is not an actual number that you can multiply by. These are important concepts.

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.

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.

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