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We all know factorials ($n! = 1 \cdot 2 \cdot 3 \cdot \ldots \cdot n$). Is there such function (or operator, or etc...) were $n$ will be divided by all the numbers before $n$. Somthing like this:

$$n \div \cdots \div 1$$

If it exists, what is it called and how do you notate it?

  • 2
    How about $f(n)=\frac1{n!}$? – 2017-02-19
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    How do you define the quotient of $1$ and $2$ for example, if you were to define such a function? This definition seems somewhat unclear. – 2017-02-19
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    Question is quite unclear. Can you elaborate a bit more? – 2017-02-19

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Division is not a commutative operation, meaning a/b does not equal b/a ( unless b=+-a, both not equal to zero). Thus, the expression n ÷ (n-1) ÷ (n-2) ÷ ...÷ 2 ÷ 1 does not make any sense unless we: 1. Take use of Pemdas (order of operations), or 2. Insert parantheses in desired location. If we use pemdas, the expression n ÷ (n-1) ÷ (n-2) ÷ ...÷ 2 ÷ 1 is equal to n/(n-1)! Here, n is assumed to be a natural number.