discrete domain
a set of input values that consists of only certain numbers in an interval
In mathematics, a function is said to have a discrete domain if its set of possible inputs or values is a countable or finite set. This means that the function can only take on certain specific values and cannot take on any value between them.
For example, consider the function f(x) = {1, 2, 3} for x ∈ {0, 1, 2} which means the function takes the input 0 and maps it to the output 1, takes the input 1 and maps it to the output 2, and takes the input 2 and maps it to the output 3. Here, the domain of the function is finite and consists of the set {0, 1, 2}.
Another example of a function with a discrete domain is the floor function, which rounds down any input to the nearest integer. The domain of this function consists of all real numbers, but the function only takes on integer values.
In summary, a discrete domain occurs when a function can only take on certain specific values due to the countable or finite set of its possible inputs or values.
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