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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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