Difference
Elementary
Think of two numbers, one subtracted from the other. The difference of the two numbers is the result of the subtraction: $7 - 3 = 4$, so the difference of $7$ and $3$ is $4$.
High school
Consider two numbers $a$ and $b$. The difference of $a$ and $b$ is the result $a - b$ of subtraction. It depends on the order and can be negative: $3 - 7 = -4$.
Examples
Examples
-
$3 - 7 = -4$
Elementary
$3 - 7 = -4$ is a difference because it is the result of a subtraction.
-
$9.8 - 9.81 = -0.01$, for a measured value $9.8$ and true value $9.81$
Elementary
$9.8 - 9.81 = -0.01$ is a difference, because it is the result of a subtraction.
Non-examples
Things that may be mistaken for examples.
-
$\setdef{1, 2, 3} \setminus \setdef{2} = \setdef{1, 3}$
Elementary
$\setdef{1, 2, 3} \setminus \setdef{2}$ is not a difference of numbers, because removing elements is not subtraction.
Distinctions involving this term
- Types of difference: Many quantities compare two things by “how far apart” they are. A difference is the result of subtraction and can be negative. No distance is negative. An error compares an approximation with the truth, a change compares the end with the start, and a set difference removes elements.