(22nd-April-2020)
Algebraic variables are symbols.
Internal to a computer, a symbol is just a sequence of bits that can be distinguished from other symbols. Some symbols have a fixed interpretation, for example, symbols that represent numbers and symbols that represent characters. Symbols that do not have fixed meaning appear in many programming languages. In Java, starting from Java 1.5, they are called enumeration types. Lisp refers to them as atoms. Usually, they are implemented as indexes into a symbol table that gives the name to print out. The only operation performed on these symbols is equality to determine if two symbols are the same or not.
To a user of a computer, symbols have meanings. A person who inputs constraints or interprets the output associates meanings with the symbols that make up the constraints or the outputs. He or she associates a symbol with some concept or object in the world. For example, the variable HarrysHeight, to the computer, is just a sequence of bits. It has no relationship to HarrysWeight or SuesHeight. To a person, this variable may mean the height, in particular units, of a particular person at a particular time.
A discrete variable is one whose domain is finite or countably infinite. One particular case of a discrete variable is a Boolean variable, which is a variable with domain {true, false}.
If X is a Boolean variable, we write X=true as its lower-case equivalent, x, and write X=false as ¬x. We can also have variables that are not discrete;
for example, a variable whose domain corresponds to a subset of the real line is a continuous variable.
The variable Class_time may denote the starting time for a particular class. The domain of Class_time may be the following set of possible times:
dom(Class_time)={8, 9, 10, 11, 12, 1, 2, 3, 4, 5}.
The variable Height_joe may refer to the height of a particular person at a particular time and have as its domain the set of real numbers, in some range, that represent the height in centimeters. Raining may be a Boolean random variable with value true if it is raining at a particular time.
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