# Function vs Superadditive - What's the difference?

## As a noun function

is what something does or is used for.

## As a verb function

is to have a function.

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

# function

## English

### Noun

(en noun)
• What something does or is used for.
• * {{quote-magazine, year=2013, month=May-June, author= Katrina G. Claw
• , title= Rapid Evolution in Eggs and Sperm , volume=101, issue=3, magazine=(American Scientist) , passage=Many genes with reproductive roles also have antibacterial and immune functions , which indicate that the threat of microbial attack on the sperm or egg may be a major influence on rapid evolution during reproduction.}}
• A professional or official position.
• (senseid)An official or social occasion.
• A relation where one thing is dependent on another for its existence, value, or significance.
• (mathematics) A relation in which each element of the domain is associated with exactly one element of the codomain.
• (computing) A routine that receives zero or more arguments and may return a result.
• (biology) The physiological activity of an organ or body part.
• (chemistry) The characteristic behavior of a chemical compound.
• (anthropology) The role of a social practice in the continued existence of the group.
• #### Synonyms

* (what something does or is used for) aim, intention, purpose, role, use * (professional or official position) occupation, office, part, role * (official or social occasion) affair, occasion, social occasion, social function * many-to-one map, many-to-one mapping, mathematical function, operation, transformation * procedure, routine, subprogram, subroutine

#### Hypernyms

* (mathematics) relation

### Verb

(en verb)
• to have a function
• to carry on a function; to be in action
• #### Synonyms

* (to have a function) officiate, serve * (to carry on a function) go, operate, run, work

#### Antonyms

* (to carry on a function) malfunction

• Knot genus is superadditive under band sum because $g\left(K_1\sharp_bK_2\right)\ge g\left(K_1\right)+g\left(K_2\right)$.