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Thu Nov 15 12:10:52 PST 2012

Contents

1. These pages are owned by Dr. Richard J. Botting in the School of Computer Science and Engineering, CSUSB.

2. Please make links and references to this material. As a rule each section heading, declaration, definition, axiom and labeled formula is an anchor that you are invited to link to.

3. These files can copied in part or whole and distributed freely for any non-profit purpose.

4. If you want to make a profit out of the copy please contact me by email so we can negotiate a small contribution to the upkeep of this web site.

5. All copies must include a copy of this notice, in its entirety.

6. Up to date copies of the original can be got free from [ http://cse.csusb.edu/dick/maths/ ]

7. Contact me via [ mailme.html ] or by mail to Dr. Richard J. Botting, California State University, San Bernardino, 5500 State University Parkway, CA 92407.

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 might be described by Net{radius:Positive Real, center:Point, area:=π*radius^2, ...}.

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

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

Glossary

9. 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).
10. given::reason="I've been told that...", used to describe a problem.
11. given::variable="I'll be given a value or object like this...", used to describe a problem.
12. goal::theorem="The result I'm trying to prove right now".
13. goal::variable="The value or object I'm trying to find or construct".
14. 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.
15. hyp::reason="I assumed this in my last Let/Case/Po/...".
16. QED::conclusion="Quite Easily Done" or "Quod Erat Demonstrandum", indicates that you have proved what you wanted to prove.
17. QEF::conclusion="Quite Easily Faked", -- indicate that you have proved that the object you constructed fitted the goal you were given.
18. RAA::conclusion="Reducto Ad Absurdum". This allows you to discard the last assumption (let) that you introduced.