A mathematical sentence is often referred to as a number sentence. Number sentences represent an equation or inequality and include numbers or variable and operands: addition, subtraction, multiplication or division.
A sentence is open if it has one or more variables. The presence of variables make it impossible to have a definite answer without knowing what the variable represents; therefore it is open to interpretation. A solution or solutions can satisfy the value of the variable or variables and make the sentence true. An open sentence can also be found to have no solution.
Open sentences need at least one variable, such as 3x = 4 + y; 80 = 8z; and 2a + 6 = b + c. These are examples of open sentences because the solutions to the variables x, y, z, and a, b, c, respectively are unknown as the equations are written. Numbers can replace the unknowns to make the sentences true.
Alternatively, math sentences can be closed. A closed math sentence has no unknowns. An example of the closed math sentence is 2 + 2 = 4; all of the values are given. A closed sentence can be true or false as written. Functions are another type of math sentence. The values in functions are unknown and can be satisfied by a series of values. An example of a function is f (x) = x + 4; the relationship in a function can be many values to one or one to one.