Over a million developers have joined DZone.
{{announcement.body}}
{{announcement.title}}

DZone's Guide to

# Mutually Odd Functions

· Big Data Zone ·
Free Resource

Comment (0)

Save
{{ articles[0].views | formatCount}} Views

Hortonworks Sandbox for HDP and HDF is your chance to get started on learning, developing, testing and trying out new features. Each download comes preconfigured with interactive tutorials, sample data and developments from the Apache community.

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?

Hortonworks Community Connection (HCC) is an online collaboration destination for developers, DevOps, customers and partners to get answers to questions, collaborate on technical articles and share code examples from GitHub.  Join the discussion.

Topics:

Comment (0)

Save
{{ articles[0].views | formatCount}} Views

Published at DZone with permission of

Opinions expressed by DZone contributors are their own.