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:
Hope these questions were fun!
- 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.