Expressions are composed of numbers, operators, number grouping symbols (parentheses), free variables and constrained variables through a meaningful arrangement, and numerical values can be obtained. Constraint variables are given a numerical value in the expression, while free variables can give a numerical value outside the expression.

In the process of expression transformation, we must know the priority order of various operations, so that the transformed expression can meet the operational requirements of mathematical formulas. The priority order of operations is: parentheses → function → power → multiplication and division → addition and subtraction → character concatenation operator → relational operator → logical operator.

The meaning of expression

Give free variables some numbers, and you can give an expression a value, even though the expression may not define a value for some free variables. So an expression represents a function. The input of the function is the fixed value of free variables, and the output is the numerical value generated by the expression factor.

For example, the expression x/y fixes free variables x and y at 10 and 5 respectively, and its output is the number 2; But when the value of y is 0, it is not defined. The assignment of expression is related to the definition of operator and the domain of numerical value.

If the two expressions are equivalent, that is to say, for any fixed value of free variables, the outputs of the two expressions are the same, that is, they represent the same function.

The expression must be well-formed. In other words, each operator must have the right number of inputs in the right place. For example, expression 2+3 is a combination; However, the expression *2+ is not grammatical, at least not a general representation of arithmetic.