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MATHS is an attempt to free mathematical notation from the tyrany
of blackboards and dead trees. I'm searching for a way to
record ideas quickly, cheaply, simply, on simple devices,
and then calculate with them. MATHS shows my current
best practice. It is a work in progress...
sometimes in regress.
A key discovery in this search was the power of hypertext links. They let you connect a symbol to its meaning. They can connect a theorem to its proof, or a premise to its statement. The next idea was to give symbolic names to mathematical and logical systems and to link these together. So a short name for a piece of mathematics can be linked to a full description of it.
As a result any set of assumptions and notation can be linked into another document. I hoped that this would be useful. It lets you reuse earlier ideas. A side effect has been the generation of many pages that document existing mathematics and logical systems.
I'd like them to be used.
How to use this site
For a quick glance at a cheatsheet of abbreviations see
[ intro_standard.html ]
which lists some of the ways of making formulas.
Here are some suggestions for using this site: [ How to use the maths site in home ]
You can seach the site for any defined term, theorem, formula, declaration, etc etc:
Or you can brouse the topics by subject at:
You can submit suggestions of material to be added:
Why
The following explains why this site exists:
[ 10_manifesto.mth ]
(source)
[ 10_manifesto.html ]
(HTML)
and
[ rjb9Xb.discrete.html ]
. . . . . . . . . ( end of section Index to the MATHS site) <<Contents | End>>
More on MATHS
. . . . . . . . . ( end of section More on MATHS) <<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 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