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
Logical Approach to Discrete Math'.
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
- 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.
This page is brought to you by Marnix Klooster, and is part of his home page.
Feel free to e-mail me with comments on the form and content of this page.
Changes to calc/calc-not.html:
Sat Apr 30 09:32:00 MEST 2005 Marnix Klooster <email@example.com>
* 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