. Notes on MATHS Notation
Special characters are defined in
.See http://www.csci.csusb.edu/dick/maths/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
.See http://www.csci.csusb.edu/dick/maths/logic_25_Proofs.html#Block Structure
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
.See http://www.csci.csusb.edu/dick/maths/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:=\pi*radius^2, ...}.
For a complete listing of pages in this part of my site by topic see
.See http://www.csci.csusb.edu/dick/maths/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
.See http://www.csci.csusb.edu/dick/maths/logic_0_Intro.html
plus sets, functions, relations, and other mathematical extensions.
For a more rigorous description of the standard notations
see
STANDARD::=http://www.csci.csusb.edu/dick/maths/math_11_STANDARD.html
. Glossary
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).
given::reason="I've been told that...", used to describe a problem.
given::variable="I'll be given a value or object like this...", used to describe a problem.
goal::theorem="The result I'm trying to prove right now".
goal::variable="The value or object I'm trying to find or construct".
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.
hyp::reason="I assumed this in my last Let/Case/Po/...".
QED::conclusion="Quite Easily Done" or "Quod Erat Demonstrandum", indicates that you have proved what you wanted to prove.
QEF::conclusion="Quite Easily Faked", -- indicate that you have proved that the object you constructed fitted the $goal you were given.
RAA::conclusion="Reducto Ad Absurdum". This allows you to discard the last
assumption ($let) that you introduced.