Arithmetic operations (addition, subtraction, etc.) involve a potentially infinite number of integer values.

• -∞, ... , -2, -1, 0, 1, 2, ... , ∞

Note: In math, integers are infinite. In computers, integers are of finite size.

Only two values are needed for two-value logic, so it must be easier than integer arithmetic.

Often, 1 is used for true and 0 is used for false.

Thus, truth table logic using two values must be simpler than arithmetic operations and logic.

Logical operations, sometimes called Boolean operations after George Boole (Founder of Boolean logic) (1820-1898), are operations that involve two values, true and false.

Two values are needed for two value logic. Here are some examples.

• True and False, t and f
• 1 and 0
• yes and no, y and n, yea and nay
• on and off
• high and low, h and l

Double-edged swords have a true edge (very sharp) and a false edge (not so sharp).

• If you are not sad/mad, you are happy.

• If you are not happy, you are sad/mad.

Magnets have opposite polarities, called poles.

Magnetic media, such as fixed/floppy disks, use one polarity for 1 and the other for 0.

Optical media, such as CD-ROM's, use high or low reflectivity as two values.

The high or low current or voltage can be used as 0 and 1.

The literal names true and false are the simplest form of what are called logical expressions.

A literal literally expresses a value and cannot be simplified. In this case, the expression true expresses the value true and the expression false expresses the value false.

Be aware that mathematicians often call an expression a formula while computer scientists often call a formula an expression.

Since we have two distinct values,

• true is always true,
• true can never be false,
• false is always false, and
• false can never be true.

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