# Calculational proofs and notations

What is a calculational solution, or a calculational proof,
or an equational solution, or an equational proof?
For now I'll simply point you to
'A
Logical Approach to Discrete Math'.
## Notations

I use the notations from the above-mentioned book, with
the following ASCII-zations:
- Universal and existential quantification is written as A and E.
- Equivalence is written as ==, and inequivalence as =/=.
Note that these operators are associative, and even
mutually associative: (P == Q) =/= R is equivalent to
P == (Q =/= R).
- Implication is written as =>, and reverse
implication as <=. (Yes, this is an ambiguity
with the 'at most' operator, which I also write
as <=. Let me know if you have a solution for
this.)
- Logical 'and' and 'or' are written as /\ and \/.
- Logical negation is written as !.
- Function application ('the f of x') is written using
an infix dot, as f.x.
- 'x is an element of set s' is also written as s.x: a set
is seen as a function that returns a boolean true when
the value is in the set, and false otherwise.

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Changes to calc/calc-not.html:
Sat Apr 30 09:32:00 MEST 2005 Marnix Klooster <myfirstname.mylastname@solcon.nl>
* Updated links to Gries' book 'A Logical Approach to Discrete Math'.
Sat Oct 30 12:38:39 MEST 2004 Marnix Klooster
* Move from CVS to darcs: do not show the CVS date anymore.
Thu Feb 7 19:43:35 MET 2002 marnix
* Updated all files to use the m4 template
Wed Sep 5 21:20:00 MEST 2001 marnix
* Made explicit that last changed date is in GMT
Wed Sep 5 21:08:51 MEST 2001 marnix
* Now 'last changed' is on its own line
Wed Sep 5 10:10:47 MEST 2001 marnix
* Added date last changed
Wed Sep 5 08:50:24 MEST 2001 marnix
* Initial revision