# Superadditive vs Subadditive - What's the difference?

superadditive | subadditive | Antonyms |

## As adjectives the difference between superadditive and subadditive

is that superadditive is (mathematics|of a function) such that the image of a sum is at least the sum of the images of the summands while subadditive is (of a function) such that the image of a sum is at most the sum of the images of the summands.

# superadditive

## English

### Adjective

(-)
• (mathematics, of a function) Such that the image of a sum is at least the sum of the images of the summands.
• Knot genus is superadditive under band sum because $g\left(K_1\sharp_bK_2\right)\ge g\left(K_1\right)+g\left(K_2\right)$.

#### Antonyms

* subadditive

# subadditive

## English

### Adjective

(-)
• (of a function) Such that the image of a sum is at most the sum of the images of the summands.
• The square-root function is subadditive under addition because $\sqrt\left\{a+b\right\}\le\sqrt a+\sqrt b$.

#### Antonyms

* superadditive