I'm having no luck

[where_was_i]

I'm in a basic sets and logic course, and we're working through induction. I'm supposed to prove: (∀n ∈ N)(Σ r.r! = (n+1)! - 1), where the lower bound is r=1, and the upper is n, and N is the natural numbers. The only thing is that I have no idea how r.r! works. Any help I'd appreciate.

Comments

[fiberpunk]

What does r.r! even mean?

[where_was_i]

It may be a misprint in the book. But my first thought was something like (1.1)! for r=1 or (6.6)! for r=6, but I think the only function that covers that is well beyond the scope of the book.

[fiberpunk]

I haven't seen notation like that before. If your book hasn't defined it, it's probably worth shooting an email to your instructor.

[mathic]

I'm amused how no one else has thought of this yet, multiplication dot instead of period dot.

A few examples just to check?

nLeft hand sideRight hand side
111
21 + 4 = 56 - 1= 5
31 + 4 + 18 = 2324 - 1 = 23

(hehehe, I just learned how to put tables on webpages... so coooooolllllzzzz)

So I think it's safe to assume it's a product dot rebelling against the man

[lsur]

r times factorial r

Try wikipedia:

http://en.wikipedia.org/wiki/Permutation as well as the article on factorials (which is probably overkill). Looks like you have to rearrange the permutation formula.

[where_was_i]

Yeah, thanks, everyone. I figured it out after playing aroud with it a little. The dot is supposed to be a multiplication sign.

[lsur]

That's a common usage, here at least. Saves cluttering the page with 'x's.

[filosophicphool]

alt + 249 = ∙

[where_was_i]

Hah, I know the 'dot' to mean 'multiply'. I'm just used to seeing it in the middle of the text row, not where a decimal or persiod would be. Thanks, though!