A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

why does is the integral form of n!(factorial)?

  • This Question is Closed
  1. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    wups, what is*

  2. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    The factorial function may be represented by a special function called, the gamma Function. You can't perform calculus on the factorial.

  3. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Have you heard of that?

  4. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yes, but we are working with sequences/series, and are comparing the factorial with other integrals but he said that 0! = 1 and said to just believe him. Then he continued to write an integral form for n! which i believe is the gamma function.

  5. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    0! is 1 because we *define* it to be the case. It comes from permutations in combinatorics. If you have n objects and you're taking them r at a time, you have the total number of ways for doing this as,\[^nP_r=n \times (n-1) \times (n-2) \times ...\times (n-r+1)\]If we now multiply this expression by 1, but in the form,\[1=\frac{(n-r)!}{(n-r)!}\]we get\[^nP_r=\frac{n \times (n-1) \times (n-2) \times ...\times (n-r+1)(n-r)!}{(n-r)!}\]\[=\frac{n!}{(n-r)!}\]Now, if we have n objects and we want to arrange things in order n ways, we'd have\[^nP_n=n!=\frac{n!}{(n-n)!}=\frac{n!}{0!}\]For this to be true, we define\[0!=1\]

  6. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Ok, so 1=0! rather than 0!=1. Think im gonna have to take some high level courses till i get to this but thanks, was interesting. You are very insightful.

  7. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    No probs.

  8. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.