Explanation of borders in the manual

The explanation includes the limit case of maxinteger being a border.
It also avoids the term "natural", which might include large floats
with natural values.

manual/manual.of

@@ -1980,15 +1980,20 @@ character is one byte.)
 
 The length operator applied on a table
 returns a @x{border} in that table.
-A @def{border} in a table @id{t} is any natural number
+A @def{border} in a table @id{t} is any non-negative integer
 that satisfies the following condition:
 @verbatim{
-(border == 0 or t[border] ~= nil) and t[border + 1] == nil
+(border == 0 or t[border] ~= nil) and
+(t[border + 1] == nil or border == math.maxinteger)
 }
 In words,
-a border is any (natural) index present in the table
+a border is any positive integer index present in the table
-that is followed by an absent index
+that is followed by an absent index,
-(or zero, when index 1 is absent).
+plus two limit cases:
+zero, when index 1 is absent;
+and the maximum value for an integer, when that index is present.
+Note that keys that are not positive integers
+do not interfere with borders.
 
 A table with exactly one border is called a @def{sequence}.
 For instance, the table @T{{10, 20, 30, 40, 50}} is a sequence,
@@ -1997,12 +2002,9 @@ The table @T{{10, 20, 30, nil, 50}} has two borders (3 and 5),
 and therefore it is not a sequence.
 (The @nil at index 4 is called a @emphx{hole}.)
 The table @T{{nil, 20, 30, nil, nil, 60, nil}}
-has three borders (0, 3, and 6) and three holes
+has three borders (0, 3, and 6),
-(at indices 1, 4, and 5),
 so it is not a sequence, too.
 The table @T{{}} is a sequence with border 0.
-Note that non-natural keys do not interfere
-with whether a table is a sequence.
 
 When @id{t} is a sequence,
 @T{#t} returns its only border,
@@ -2016,7 +2018,7 @@ the memory addresses of its non-numeric keys.)
 
 The computation of the length of a table
 has a guaranteed worst time of @M{O(log n)},
-where @M{n} is the largest natural key in the table.
+where @M{n} is the largest integer key in the table.
 
 A program can modify the behavior of the length operator for
 any value but strings through the @idx{__len} metamethod @see{metatable}.