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An inverse, without any qualification, is taken to be the multiplicative inverse. is
The inverse of a number, x (x not 0), is 1 divided by x. Any number multiplied by its inverse must be equal to 1.
There is also an additive inverse. For any number y, the additive inverse is -y. And the sum of the two must always be 0.
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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.
Why are the rational numbers under the operation of multiplication not a group?
I believe it is because 0 does not have an inverse element.
What do you call integers that add to zero?
Two numbers, which when added together result in zero, are called each other's additive inverse. That is, for two given numbers x and y, if x + y = 0, then y is the additive inverse of x and x is the additive inverse of y.
How are multiples and factors similar and different from each other?
They're both whole numbers. Factors go into numbers, numbers go into multiples. They have an inverse relationship. If A is a factor of B, then B is a multiple of A.
How are factors and multiples similar?
They have an inverse relationship in the sense that if A is a multiple of B, then B is a factor of A.They describe relationships between numbers.
