Big O Unit Notation

From Rest of What I Know

Big O Unit Notation is a variant of Big O notation that is used when you want to express a notion of 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 or is of length to mean that it is in when represented in that unit.

Formal Usage[edit]

Perhaps more formally: A measurement or quantity is said to be if:

  1. The quantity can be expressed in terms of the given unit.
  2. When expressed in that unit, the numerical value falls within the range .
  3. It is the largest such unit that satisfies conditions 1 and 2.

Examples:

  1. A 100 m race is
  2. A marathon is run in
  3. A Starbucks is away from me
  4. San Jose is away from San Francisco

Colloquial Usage[edit]

Colloquial usage weakens the bounds and allows for representing with a multiplier such as

Conversion to Other Bases[edit]

In other bases, we may use as our limits.