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Sat Oct 18 10:50:55 PDT 2008


    Holes in Documents -- FAQs

      What is a hole

      A hole is a place where a document has room to grow. Most pages on the WWW are continually changing. Computer documents tend to grow. One technique is to develop them top-down. THis means laying out the outline or structure first and filling in the details later. A hole:
      is the MATHS code to indicate such growth areas.

      Another thing that happens is that the author may be interupted or run of time, energy, or ideas; and yet still want to publish what has been written. This is again a good place to indicate a "Hole" in the document.

      What can replace a hole

      The author may replace a hole by more documentation or a set of links to other documents. Another person may not be able to do this but may have something that will fill the hole. In this case they should contact the author with the URL of the information plus enough information to make the link and assign credit.

      Such a remote document is called a plugin.

      What format should a plugin take

      You can use any format. However if you stick to the simplest forms more people will read them. Complex HTML with frames does not help readers. Niether do superfluous graphics. PDF is not as readable as Adobe thinks. Any Microsoft binary may hide code that can act like a virus or worm.

      Can I use MATHS

      Yes. The hole.html page calls the hole.php script that translates MATHS into a web page preview, and will send it to me.

      Can I use TeX

      You can... but it reduces your readership.

      Can I use XML

      Some day there will be an XML format for MATHS. I have some notes on paper listing the entities and elements. At this time XML is unstable and I wouldn't reccommend any of the existing mathematical Document Type Definitions (DTD).

      Let me know if you have a new or better one.

    . . . . . . . . . ( end of section Holes in Documents -- FAQs) <<Contents | End>>

    Notes on MATHS Notation

    Special characters are defined in [ intro_characters.html ] that also outlines the syntax of expressions and a document.

    Proofs follow a natural deduction style that start with assumptions ("Let") and continue to a consequence ("Close Let") and then discard the assumptions and deduce a conclusion. Look here [ Block Structure in logic_25_Proofs ] for more on the structure and rules.

    The notation also allows you to create a new network of variables and constraints. A "Net" has a number of variables (including none) and a number of properties (including none) that connect variables. You can give them a name and then reuse them. The schema, formal system, or an elementary piece of documentation starts with "Net" and finishes "End of Net". For more, see [ notn_13_Docn_Syntax.html ] for these ways of defining and reusing pieces of logic and algebra in your documents. A quick example: a circle = Net{radius:Positive Real, center:Point}.

    For a complete listing of pages in this part of my site by topic see [ home.html ]

    Notes on the Underlying Logic of MATHS

    The notation used here is a formal language with syntax and a semantics described using traditional formal logic [ logic_0_Intro.html ] plus sets, functions, relations, and other mathematical extensions.

    For a more rigorous description of the standard notations see

  1. STANDARD::= See http://www.csci.csusb.edu/dick/maths/math_11_STANDARD.html


  2. above::reason="I'm too lazy to work out which of the above statements I need here", often the last 3 or 4 statements. The previous and previous but one statments are shown as (-1) and (-2).
  3. given::reason="I've been told that...", used to describe a problem.
  4. given::variable="I'll be given a value or object like this...", used to describe a problem.
  5. goal::theorem="The result I'm trying to prove right now".
  6. goal::variable="The value or object I'm trying to find or construct".
  7. let::reason="For the sake of argument let...", introduces a temporary hypothesis that survives until the end of the surrounding "Let...Close.Let" block or Case.
  8. hyp::reason="I assumed this in my last Let/Case/Po/...".
  9. QED::conclusion="Quite Easily Done" or "Quod Erat Demonstrandum", indicates that you have proved what you wanted to prove.
  10. QEF::conclusion="Quite Easily Faked", -- indicate that you have proved that the object you constructed fitted the goal you were given.
  11. RAA::conclusion="Reducto Ad Absurdum". This allows you to discard the last assumption (let) that you introduced.