# Mutually Odd Functions

# Mutually Odd Functions

Join the DZone community and get the full member experience.

Join For Free**How to Simplify Apache Kafka. Get eBook.**

The floor of a real number *x* is the largest integer *n ≤ x*, written ⌊x⌋.

The ceiling of a real number *x* is the smallest integer *n ≥ x*, written ⌈x⌉.

The floor and ceiling have the following symmetric relationship:

⌊-*x*⌋ = -⌈*x*⌉

⌈-*x*⌉ = -⌊*x*⌋

The floor and ceiling functions are not odd, but as a pair they satisfy a generalized parity condition:

*f*(-*x*) = -*g*(*x*)*g*(-*x*) = -*f*(*x*)

If the functions f and g are equal, then each is an odd function. But in general f and g could be different, as with floor and ceiling.

Is there an established name for this sort of relation? I thought of “mutually odd” because it reminds me of mutual recursion.

Can you think of other examples of mutually odd functions?

**12 Best Practices for Modern Data Ingestion. Download White Paper.**

Published at DZone with permission of John Cook , DZone MVB. See the original article here.

Opinions expressed by DZone contributors are their own.

## {{ parent.title || parent.header.title}}

{{ parent.tldr }}

## {{ parent.linkDescription }}

{{ parent.urlSource.name }}