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Factorial!

We know 5! = 5x4x3x2x1 = 120. Nonetheless, many students still think that it means that you vocalize the digit 5 with emphasis.

But, ask your students to consider these questions:

  • Why does 0! = 1? That is, is 0! =1 a matter of definition or can it be proved?
  • Why is a factorial symbol used? That is, what is its history in a mathematical context?
  • How would you determine things such as 3.4! or (-2)! or (-2.5)! or (3+2i)!? Note: these unusual expressions have actual values.
  • What is the meaning of n!! or n!!!? Note: Mathematicians do not agree on this, as I know of two quite different definitions, both found in published form.
Hope these questions were fun!