I’ve seen at least two phrases to describe a fixed difference between two numbers, i.e., “constant difference” and “common difference.”

For example, if Sibling A is 10 years older than Sibling B today, you can expect that the difference in their ages will always be 10 years.

Some questions:

  • Are these two phrases always interchangeable, or is there some nuance that would be good for an educator or student to understand?
  • Does this principle go by any other names?
  • $\begingroup$ for questions on mathematical terminology, consider asking math exchange $\endgroup$
    – okzoomer
    Nov 27 '21 at 12:55
  • $\begingroup$ Okay. I’ll consider re-posting my question there. $\endgroup$
    – EJ Mak
    Nov 27 '21 at 15:38
  • $\begingroup$ Cross-posted to MSE. $\endgroup$
    – ryang
    Nov 27 '21 at 18:23
  • $\begingroup$ Neither constant difference nor common difference is terminology in common use among professional mathematicians or those teaching at the university level. The proliferation at the primary level of ad hoc terminologies to describe very specific situations is often no productive, and often serve to generate confusion. There is little to be gained by formalizing representations of patterns that do not frequently occur in practice. The distinction made here is worth making, but possibly not worth formalizing. $\endgroup$
    – Dan Fox
    Dec 19 '21 at 10:25
  1. There is a constant difference between A's and B's ages.

    Here, the value of interest is constant as the input, time, varies.

  2. There is a common difference between successive terms of sequence S.

    Here, the value of interest is common across varying objects of comparison.

    But I could equally say there is a constant difference between successive terms (as I vary the index). Here, the disparity between constant difference and common difference is just a matter of framing and emphasis, and isn't important.

  • $\begingroup$ Can you expand on 1 and 2? I’m close to understanding, but I’m not there yet. $\endgroup$
    – EJ Mak
    Nov 27 '21 at 15:37
  • 1
    $\begingroup$ @EJMak 1. A value being constant can be thought of as some function being identically constant. 2. A value being common can be thought of as some property being shared by different entities. $\endgroup$
    – ryang
    Nov 27 '21 at 16:52

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