An equation is an assertion that two mathematical expressions are equal as in:
- left-hand-side = right-hand-side
The equality can be justified because
- the statement is a Mathematical identity or
- the statement is a Mathematical definition or
- the statement describes the relationship between two or more expressions.
- a + b = b + a
is justified because the addition operation is commutative. This equation is the symbolic equivalent of that property. On the other hand, the equation
- y = a + b x
is an assertion about the symbols it mentions.
- Letters from the beginning of the alphabet like a, b, ... are convenctionally considered as constants in the context of the discussion at hand.
- Letters from end of the alphabet, x,y,z are usually considered variables, that is, their values may change within the discussion.