Editing Big O Unit Notation

[[Big O Unit Notation]] is a variant of [[wikipedia:Big O notation|Big O notation]] that is used when you want to express a notion of [[wikipedia:order of magnitude|order of magnitude]]. You can usually differentiate these two concepts by the fact that Big O Notation is expressed in terms of functions whereas [[Big O Unit Notation]] is expressed in terms of units.

One writes that some process or action takes <math>O(milliseconds)</math> or is of length <math>O(kilometres)</math> to mean that it is in <math>[0.5, 100)</math> when represented in that unit.

== Formal Usage ==

Perhaps more formally: A measurement or quantity is said to be <math>O(unit)</math> if:

# The quantity can be expressed in terms of the given unit. 
# When expressed in that unit, the numerical value falls within the range <math>[0.5, 100)</math>. 
# It is the largest such unit that satisfies conditions 1 and 2.

Examples:

# A 100 m race is <math>O(seconds)</math>
# A marathon is run in <math>O(hours)</math>
# A Starbucks is <math>O(meters)</math> away from me
# San Jose is <math>O(kilometers)</math> away from San Francisco

== Colloquial Usage ==

Colloquial usage weakens the bounds and allows for representing with a multiplier such as <math>O(100 km)</math>

[[Category:Concepts]]