Beefy Boxes and Bandwidth Generously Provided by pair Networks
laziness, impatience, and hubris
 
PerlMonks  

Comment on

( #3333=superdoc: print w/ replies, xml ) Need Help??
You write: If you take a definition from a random hit for "modulo mathematical definition" taken from the WWW, for instance, you'll find the definition: Two numbers a and b are said to be equal or congruent modulo N iff N|(a-b), i.e. iff their difference is exactly divisible by N. Usually (and on this page) a,b, are nonnegative and N a positive integer. We write a = b (mod N). Note that the difference has to be divisible by N. Yes, and the difference between no two different integers is divisible by zero. Therefore all integers are in different congruence classes mod 0, which is another way of saying that x mod 0 = x, as the original poster claimed. Although of course it's a matter of definition whether (1) an integer is then congruent to itself mod 0 and (2) the mod "operator" is actually that closely related to the mod "arithmetic" that it returns the name of the congruence class under arithmetic mod that number. % is probably better called "remainder" than mod, anyhow, and again it makes sense for x % 0 to be x when you talk about remainders. No matter how often you subtract zero, x remains... (but that's the same argument others have made).

In reply to Re^4: 0 illegal modulus? by Anonymous Monk
in thread 0 illegal modulus? by nella

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!
  • 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, 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, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • Outside of code tags, you may need to use entities for some characters:
            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.
  • Log In?
    Username:
    Password:

    What's my password?
    Create A New User
    Chatterbox?
    and the web crawler heard nothing...

    How do I use this? | Other CB clients
    Other Users?
    Others contemplating the Monastery: (9)
    As of 2014-10-24 13:01 GMT
    Sections?
    Information?
    Find Nodes?
    Leftovers?
      Voting Booth?

      For retirement, I am banking on:










      Results (131 votes), past polls