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Distinct
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Two or more things are distinct if no two of them are the same thing. In

mathematics, two things are called distinct if they are not

equal.

## Example

A

quadratic equation over the

complex numbers sometimes has two

roots.
The equation
x2 ? 3x + 2 = 0

factors as
(x ? 1)(x ? 2) = 0
and thus has as roots x = 1 and x = 2. Since 1 and 2 are not equal, these roots are distinct.
In contrast, the equation:
x2 ? 2x + 1 = 0
factors as
(x ? 1)(x ? 1) = 0
and thus has as roots x = 1 and x = 1. Since 1 and 1 are (of course) equal, the roots are not distinct; they coincide.
In other words, the first equation has distinct roots, while the second does not. (In the general theory, the

discriminant is introduced to explain this.)

## Proving distinctness

In order to

prove that two things x and y are distinct, it often helps to find some

property that one has but not the other. For a simple example, if for some reason we had any doubt that the roots 1 and 2 in the above example were distinct, then we might prove this by noting that 1 is an

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