The fact that 0! == 1 is a logical extension of the definition of factorial: n! == n * (n - 1)!. 
    1 == 1! == 1 * (1 - 1)! == 1 * 0! == 0!

[download]
It's not an arbitrary value, it's a logical one.

But we can't do so for 0/0. Consider: 

        0 
    lim - == 0
   x->0 x 
 
but,

        x
    lim - == 1
   x->0 x
It would also mean the function x / 0 is undefined, except for the case x == 0.

Abigail

In reply to Re: What is zero divided by zero anyway? by Abigail-II
in thread What is zero divided by zero anyway? by BrowserUk

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.