Variable

Definition

A variable is a symbol that can stand for different values.

Example:

x

If:

x = 5

then x stands for 5.

If:

x = 10

then x stands for 10.

A variable is a reusable symbol whose value depends on context.

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Why Variables Exist

Variables let us describe patterns without choosing one specific value.

Example:

x + 1

This expression describes a pattern:

take some value and add 1

If x = 2:

x + 1 = 3

If x = 7:

x + 1 = 8

Variables make general reasoning possible.

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Variable vs Value

A variable is not the value itself.

Example:

x = 5

The variable is:

x

The value is:

5

The variable is a symbol that refers to the value in this context.

Variable = symbol. Value = assigned object or quantity.

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Assignment

An assignment connects a variable to a value.

Example:

x = 5

This means:

wherever x appears in this context, use 5

Expression:

x + 2

After assignment:

5 + 2 = 7

Assignment gives a variable a value in a context.

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Variables In Logic

In logic, variables can stand for objects.

Example:

Human(x)

This can be read as:

x is human

The statement depends on what x refers to.

If x = Socrates, then:

Human(Socrates)

Logical variables allow statements about unspecified objects.

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Final Summary

• A variable is a symbol that can stand for different values.
• Variables allow general expressions.
• A variable is not the same as its value.
• Assignment gives a variable a value in a context.
• In logic, variables can stand for objects inside statements.
• Variables prepare the ground for substitution and quantification.