Merge pull request #2362 from cronos2/master

Corrects some imprecisions in the "Doing math with Perl 6" article
Thanks a lot!

Author: JJ

doc/Language/math.pod6

@@ -82,7 +82,9 @@ mathematical notation.
 =head1 Arithmetic
 
 Perl 6 can do arithmetic using different data types. L<Num>, L<Rat> and
-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)>.
+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)>
+(technically, it should be noted that data types dealing with floating point number representations are not a field in the mathematical sense due to the inherent
+imprecisions of their arithmetic. However, they constitute an approximate enough, computer friendly version of such mathematical objects for most of the cases).
 The equivalent mathematical fields are:
 
 =begin table
@@ -93,12 +95,10 @@ Num              ℝ
 Complex          ℂ
 =end table
 
-The C<Int>s, although technically corresponding to Z, is not really a
-mathematical field since they are not closed under the four arithmetical
-operations, and integers do not satisfy the
-L<identity axiom|https://math.stackexchange.com/questions/2192317/set-of-integers-not-a-field/2192330>.
-However, if the integer division C<div> is used, their operations will always
-yield other integers; if C</> is used, however, in general the result will be a
+The C<Int>s or ℤ, as they're usually called in mathematics, are not a
+mathematical field but rather a ring, since they are not closed under
+multiplicative inverses. However, if the integer division C<div> is used, their operations will always
+yield other integers; if C</> is used, on the other hand, in general the result will be a
 L<Rat>.
 
 Besides, C<Int> can do infinite-precision arithmetic (or at least infinite as
@@ -120,10 +120,10 @@ mathematically:
 basic operations for L<vectors|https://en.wikipedia.org/wiki/Coordinate_vector>.
 
 =item L<C<Math::Matrix>|https://github.com/pierre-vigier/Perl6-Math-Matrix>
-operates on the L<matrix field|https://en.wikipedia.org/wiki/Matrix_field>.
+operates on L<matrices rings over numeric rings|https://en.wikipedia.org/wiki/Matrix_(mathematics)>.
 
 =item L<C<Math::Quaternion>|https://github.com/Util/Perl6-Math-Quaternion>
-operates on the L<quaternion field|https://en.wikipedia.org/wiki/Quaternion>,
+operates on the L<quaternion algebra, ℍ|https://en.wikipedia.org/wiki/Quaternion>,
 which are a generalization of complex numbers.
 
 =item L<C<Math::Polynomial>|https://github.com/colomon/Math-Polynomial> works
@@ -195,7 +195,7 @@ We can, in fact, compute the approximation to the L<golden ratio|https://en.wiki
 The L<Math::Sequences|https://github.com/ajs/perl6-Math-Sequences> module
 includes many mathematical sequences, already defined for you. It defines many
 L<sequences from the encyclopedia|https://oeis.org/>, some of them with their
-original name, such as ℤ or ℝ.
+original name, such as ℤ.
 
 Some set operators also operate on sequences, and they can be used to find out if an object is part of it:
 
@@ -208,7 +208,7 @@ generators. And we can use set inclusion operators too:
     say (55,89).Set ⊂ (1,1, * + * … * > 200); # OUTPUT: «True␤»
 
 although it does not take into account if it is effectively a subsequence, just
-the presence of the two elements here; Sets have no order, and even if you don't
+the presence of the two elements here. Sets have no order, and even if you don't
 explicitly cast the subsequence into a Set or explicitly cast it into a C<Seq>
 it will be coerced into such for the application of the inclusion operator.