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Add minor corrections such as removing dangling period in headers,
fixing typo, removing C<> from table components given that are not
rendered (NYI), etc.
Copy file name to clipboardExpand all lines: doc/Language/math.pod6
+12-12Lines changed: 12 additions & 12 deletions
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=SUBTITLEDifferent mathematical paradigms and how they are implemented in this language
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=head1Sets.
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=head1Sets
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Perl 6 includes the L<Set> data type, as well as support for
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L<most set operations|/language/setbagmix#Set/Bag_Operators>.
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=endcode
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In this code, which uses the L<empty set|/language/setbagmix#term_%E2%88%85>
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which is already defined by Perl 6, not only we check if the equalities in the
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which is already defined by Perl 6, not only do we check if the equalities in the
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algebra of sets hold, we also use, via L<sigilless variables|/language/variables#index-entry-\_(sigilless_variables)> and the
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Unicode form of the set operators, expressions that are as close as possible to
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the original form; C<A ∪ U === U>, for example, except for the use of the
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L<value identity operator <===>|/routine/===> is very close to the actual
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mathematical expression in the L<Wikipedia entry|https://en.wikipedia.org/wiki/Algebra_of_sets>.
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We can even test de Morgan's law, as in the code below:
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We can even test De Morgan's law, as in the code below:
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=begincode
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my @alphabet = 'a'..'z';
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We declare C<⁻> as the I<complement> operation, which computes the symmetrical
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difference ⊖ between the Universal set C<U> and our set. Once that is declared,
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it is relatively easy to express operations such as the complementary of the
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union of A and B C<(A ∪ B)⁻>, with a notation that is very close to the original
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union of A and B,C<(A ∪ B)⁻>, with a notation that is very close to the original
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mathematical notation.
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=head1Arithmetic.
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=head1Arithmetic
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Perl 6 can do arithmetic using different data types. L<Num>, L<Rat> and
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L<Complex> can all operate as a L<field under the operations addition, subtraction, multiplication and division|https://en.wikipedia.org/wiki/Field_(mathematics)>.
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L<Complex> can all operate as a L<field under the operations of addition, subtraction, multiplication and division|https://en.wikipedia.org/wiki/Field_(mathematics)>.
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