Statement
A sentence that is definitely true or definitely false, never both. Maths proofs are built from statements.
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Analogy
A light switch: it is on or off, with no in-between.
Example
'7 is prime' is true.'9 is prime' is false, since 9 = 3 x 3.'x + 2 = 5' is not a statement yet.It is true for x = 3, false for x = 4.
In practice
Before you try to prove something, check it is a statement. 'x + 2 = 5' only becomes one once x is chosen.
Questions people ask
What is the difference between a statement and an open sentence?
A statement has a fixed truth value: true or false. An open sentence such as 'x is even' contains a free variable, so it has no truth value until you pick x or quantify it. Replacing x with 4 gives a true statement; with 5, a false one.
Can a statement be both true and false in maths?
No. Classical mathematics assumes every statement is exactly one of true or false. This is why proof by contradiction works: if assuming something leads to both a statement and its opposite being true, the assumption cannot hold. Ambiguous everyday sentences are not allowed as maths statements, though.