I have seen both usages, and want to learn how to choose the appropriate option.

  • Could you provide the context that you want to use it in? – Nicole Mar 10 '15 at 18:30
  • @Nicole My bad. I had mostly algorithms analysis and design in mind, but dang's answer seems to identify a pretty general pattern. So for my field, an example would be an upper bound ON the running time of an algorithm, which (the running time) could have an upper bound OF O(n). – GreenhouseVeg Mar 10 '15 at 21:31

The usage I have most often seen in quantitative technical fields is that there is an upper bound on a variable. And if you use "an upper bound of..." you are referring to that limit, rather than the variable that is being limited.

For example, "there is an upper bound of 50 miles per hour on my car's velocity."

See Mathwords.com for "upper bound of" and this article ("A Simple Upper Bound on the Redundancy of Huffman Codes") for many, many examples of "upper bound on" usage.

  • Followed the sound advice of @EdwinAshworth. Thanks! – dang Mar 10 '15 at 15:49

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