Pedmas questions revisited

Where does factorial fit in the order of operations?

Is n+1!=(n+1)!? I think not.

Is 3n!=(3n)!? Now I’m not so sure.

What about 3^n!=(3^n)! ?

So is it PEMDFAS?





4 responses to “Pedmas questions revisited

  1. Parentheses are always first. Factorial is in the next group.

    See in the programming language section.

  2. I wonder if Christopher was really asking this question.

    My thinking is that the ! applies to the term to the left (as with exponents). So, 2*3! = 2*6 =12 whereas (2*3)! = 6! = 720. But if my audience finds the first expression ambiguous, maybe it’s up to me to communicate my intended meaning more clearly as 2*(3!).

    Interestingly, to me at least, is that whether we’re talking factorial or exponents, it is my understanding of brackets as grouping symbols, not BEDMAS or BFEDMAS, that determined how I evaluated the expressions above. It’s similar for something like 2*(3 + 4). Grouping, not following a checklist.

    What about absolute value? logs? sine? nCk? What might that mnemonic look like? Or, maybe just an F to represent any function? Just think about how the F in PFEMDAS or PEMDFAS could enhance ‘Please Excuse My Dear Aunt Sally’.

  3. Fun fact: In the U.K., it’s called BIDMAS (Brackets, Indices). One could postulate that factorial is an index, much like an exponent or root.

  4. This comment came in from a dear colleague via email:

    Simple answer: Factorial is one of many grouping symbols so it should be ITOGSTBMA……and that is all I have to say….

    Inside to Outside Grouping Symbols then Top and Bottom then Multiplication and Addition…noting that there is always an exception. Like if addition is inside the groupuing symbol which is inside a SIN function which is divided by a factorial then cubed before subtracting PI….

    What the hell it is all crap….

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