Example · High school
Terms
| Term | This example | Why |
|---|
| expression |
✓ |
$x^2 + 1$ is an expression, because it names a number once $x$ is given.
|
| term |
✓ |
$x^2 + 1$ is a term, because $x^2 + 1$ is built from the variable $x$ and the constants $2$ and $1$ with the function symbols for squaring and addition, and $x^2 + 1$ names a number once $x$ is given a value.
|
| proposition |
✗ |
$x^2 + 1$ is not a proposition, because it has no relation sign, so it is never true or false.
|
| predicate |
✗ |
$x^2 + 1$ is not a predicate, because it has no relation sign, so it is never true or false.
|
| sentence |
✗ |
$x^2 + 1$ is not a sentence, because every sentence is a formula and $x^2 + 1$ is a term, which names a number instead of making a claim.
|
| formula logic |
✗ |
$x^2 + 1$ is not a formula, because $x^2 + 1$ is a term that names a number and makes no claim that could be true or false.
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