# What is the definition of a mathematical sentence?

Basically, a

*sentence*is a formula which is either true or false, e.g. 1 < 2 (it is true of course), 0 = 1 (this is false, but still a sentence).*[We'll assume we are working with real numbers....]*If you have variables, they must be "quantified", that is, you either say that the formula holds*for every*value of the variable, or*for some*(possibly unknown) value of the variable. 1) 1+2 = 3 2) x+2 = 3 3) x+2 = 3, for some x 4) x+2 = 3, for every x 1 is a true sentence, 2 is*not*a sentence, 3 is a true sentence (since x=1 is a solution), 4 is a false sentence (because x=0 is an example for which the formula is false). A mathematical sentence in algebra is also known as an expression. An expression can be defined as a sentence that has a number, an operation, and a letter in it. When a mathematical sentence is not in algebraic form, it just has to have two numbers and an operation.