Definition
Mathematical statement
A mathematical statement is a complete claim with a definite truth value: true or false.
What it means
It says something that can be checked. “Eight is even” is a statement. “What is eight?” is a question, so it has no truth value. An expression such as 3 + 5 has no claim at all.
Remember it
A statement makes a checkable claim.
Example
“The sum of two odd whole numbers is even” is a mathematical statement. It is true, and a proof can show why it works for every pair of odd whole numbers.
Watch for
“x > 4” is an open sentence until x is given a value or the sentence says which values are being considered.
Common mix-up
An equation can be a statement, but an expression such as 3 + 5 is not a statement because it makes no claim.
Exact meaning
A mathematical statement is a declarative mathematical sentence that, once its meanings and any needed values are fixed, is either true or false.