A good example would be integers. Also, a collection of numbers such as (0, 0.1, 0.2, 0.3, 0.4, ...) or (0, 10, 20, 40, 50, 80, ...). Actually, I believe the term "discrete" is applied to math with certain types of numbers, not to the numbers themselves. The general idea is that a certain variable can have some specific values (for example, integers), but no numbers in between.
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They are continuous.
Yes, using whole numbers.
Discrete Function - A function that is defined only for a set of numbers that can be listed, such as the set of whole numbers or the set of integers. Explicit Definition - A definition of a function by a formula in terms of the variable.
This is called a discrete set (all points isolated) or a finite set. Finite sets are always discrete.
Data that are countable values (does not need to be whole numbers). For example, 1/2, 1, 1 1/2, 2, 2 1/2, etc are discrete.