Author: lwall
Date: 2010-02-20 16:34:25 +0100 (Sat, 20 Feb 2010)
New Revision: 29790
Modified:
docs/Perl6/Spec/S03-operators.pod
Log:
[S03] cleanups suggested by nick++
Modified: docs/Perl6/Spec/S03-operators.pod
===================================================================
--- docs/Perl6/Spec/S03-operators.pod 2010-02-20 09:52:00 UTC (rev 29789)
+++ docs/Perl6/Spec/S03-operators.pod 2010-02-20 15:34:25 UTC (rev 29790)
@@ -1943,27 +1943,29 @@
For intuited numeric generators that don't involve geometric sign changes, all
values are assumed to be monotonically increasing or decreasing, as determined
-by the (up to) three values used above; if a supplied limt value is on the
+by the (up to) three values used above; if a supplied limit value is on the
"wrong" side of the first of those values, Nil is returned, even though the
limit value never matches, and never falls between two generated values.
Examples:
my $n = 0;
- 1,2,4 ... $n; # (), geometric increasing
- -1,-2 ... $n; # (), arithmetic decreasing
- 1 ... $n; # (), .succ increasing
+ 1,2,4 ... $n; # (), geometric increasing
+ -1,-2 ... $n; # (), arithmetic decreasing
+ 1 ... $n; # (), .succ increasing
For a geometric series with sign changes, the same criterion is used, but
applied only to the absolute value, and the impossibility of a limit is
evaluated by whether it's inside or outside the possible range:
- 1,-2,4 ... 0 # (), geometric alternating increasing abs
- 1,-1/2,1/4 ... 2 # (), geometric alternating decreasing abs
+ 1,-2,4 ... 0 # (), geometric alternating increasing abs
+ 1,-1/2,1/4 ... 2 # (), geometric alternating decreasing abs
-But note that both of these are infinite lists:
+But since "asymptotically approaching" is not the same as "equals", both of
+the following are infinite lists, as if you'd specified C<*> for the limit
+rather tha 0:
- 1,1/2,1/4 ... 0 # 1,1/2,1/4 ... *
- 1,-1/2,1/4 ... 0 # same as 1,-1/2,1/4 ... *
+ 1,1/2,1/4 ... 0 # like 1,1/2,1/4 ... *
+ 1,-1/2,1/4 ... 0 # like 1,-1/2,1/4 ... *
When an explicit limit function is used, it
may choose to terminate its list by returning any false value.
