Are these questions unambiguous?

Here are two very similar questions for you.

  • Is there a pair of positive integers m and n, both greater than 1, satisfying mn=9?
  • Are there two positive integers m and n, both greater than 1, satisfying mn=9?

And here are some questions about these questions (“metaquestions”?).

  • Is at least one of the questions above ambiguous?
  • Do the two questions have the same answer?
  • Might students be worried about whether or not m and n are allowed to be equal?

This issue has actually turned up in my teaching (though with a different question, and with other issues around that could cause problems).

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2 responses to “Are these questions unambiguous?

  1. Research mathematicians using a phrase such as “two integers” often allow the two integers to be the same. Citations 54, 119, 220, 229, 260, 322, 323, 338 in the Handbook of Mathematical Discourse give examples of this. (The Handbook is online: see http://www.cwru.edu/artsci/math/wells/pub/abouthbk.html) This certainly should be mentioned at appropriate times when teaching math. Sometimes college students who are fairly far along as math majors are confused by this.

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  2. Pingback: » Two Gyre&Gimble

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