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.