NAME
Number::Natural::SetTheory - set-theoretic definition of natural numbers
SYNOPSIS
use Number::Natural::SetTheory qw/:all/;
my $three = number_to_set(3);
say (scalar @$three); # says '3'
# says '0', '1', and '2'
foreach my $member (@$three)
{
say (scalar @$member);
}
# says '{{},{{}},{{},{{}}}}'
say set_to_string($three);
DESCRIPTION
For years mathematicians struggled to answer what numbers exactly are. A
satisfactory answer came out of the world of set theory. Because Perl
doesn't have sets as a first class data type, we use arrays instead. The
set theory notation for the set of the letters A, B and C is:
{ A, B, C }
The Perlish notation is:
[ 'A', 'B', 'C' ]
For the rest of this documentation, we'll use Perlish notation unless
otherwise stated. Also, it's worth noting that sets are unordered, while
arrays are ordered. This module works around that difference by simply
ignoring the order of array elements.
Anyway, so what are numbers? We define zero as the empty set:
our $zero = [];
Further natural numbers are defined as the set containing all smaller
natural numbers:
our $one = [$zero];
our $two = [$zero, $one];
our $three = [$zero, $one, $two];
# etc
This has a nice property:
scalar @$three == 3
Note that:
our $not_three = [$zero, $zero, 'Chuck Norris'];
scalar @$three == 3; # true
In the case above, the set $not_three does not represent a number at all.
This module offers a number of functions for converting between Perl
non-negative integers and the sets representing the natural numbers.
set_is_number($set, $number)
Returns true (see boolean) iff the set represents the number. Also has the
property that if $set is an actual Perl scalar integer, it returns true
iff the two numbers are equal.
number_to_set($number)
Returns the set that represents a number, given a Perl scalar integer. If
$number is not a number, then returns `undef`.
set_to_number($set)
Converts a set to a Perl scalar integer. Returns `undef` if the set does
not represent a number at all. This is the reverse of $number_to_set.
set_to_string($set)
Returns the set as a string, using number theory notation (curly
brackets).
BUGS
These functions are very recursive. I wouldn't recommend using them with
numbers greater than ten.
This module doesn't really have any use cases.
Please report any bugs to
.
SEE ALSO
.
AUTHOR
Toby Inkster .
COPYRIGHT AND LICENCE
This software is copyright (c) 2011-2012 by Toby Inkster.
This is free software; you can redistribute it and/or modify it under the
same terms as the Perl 5 programming language system itself.
DISCLAIMER OF WARRANTIES
THIS PACKAGE IS PROVIDED "AS IS" AND WITHOUT ANY EXPRESS OR IMPLIED
WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED WARRANTIES OF
MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE.