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Add minor corrections
Add minor corrections such as removing dangling period in headers, fixing typo, removing C<> from table components given that are not rendered (NYI), etc.
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doc/Language/math.pod6

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=SUBTITLE Different mathematical paradigms and how they are implemented in this language
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=head1 Sets.
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=head1 Sets
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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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=end code
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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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=begin code
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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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=head1 Arithmetic.
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=head1 Arithmetic
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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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The equivalent mathematical fields are:
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=begin table
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Perl 6 class Field
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============= ==============================================
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C<Rat>
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C<Num>
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C<Complex>
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Rat
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Num
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Complex
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=end table
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The C<Int>s, although technically corresponding to Z, is not really a
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Also strictly speaking, the Rational class that behaves like a mathematical
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field is L<FatRat>. For efficiency reasons, operating with C<Rat>s will fall
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back ton C<Num> when the numbers are big enough or when there is a big
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back to C<Num> when the numbers are big enough or when there is a big
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difference between numerator and denominator. C<FatRat> can work with arbitrary
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precision, the same as the default C<Int> class.
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@@ -152,8 +152,8 @@ L<≅|/language/operators#infix_=~=>
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=head1 Sequences
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A L<sequence|https://en.wikipedia.org/wiki/Sequence> is I<an enumerated>
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collection of objects in which repetitions are allowed>, and also a first-class
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A L<sequence|https://en.wikipedia.org/wiki/Sequence> is an I<enumerated>
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collection of objects in which repetitions are allowed, and also a first-class
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data type in Perl 6 called L<Seq>. C<Seq> is able to represent infinite
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sequences, like the natural numbers:
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doc/Language/numerics.pod6

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@@ -48,7 +48,7 @@ say (5/2).narrow; # OUTPUT: «2.5␤»
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say 1 / 10⁹⁹; # OUTPUT: «1e-99␤»
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=end code
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Perl 6 has L<FatRat> type that offers arbitrary precision fractions. How come
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Perl 6 has a L<FatRat> type that offers arbitrary precision fractions. How come
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a limited-precision L<Num> is produced instead of a L<FatRat> type in the
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last example above? The reason is: performance. Most operations are fine
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with a little bit of precision lost and so do not require the use of a more

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