Well, MRE doesn't say that those regexen are to be used to find integers -- in fact, it states: 'We don't know what these might be used for ...'.

However, if you do want to find (and extract) just integers you could employ both negative look-ahead, and negative look-behind (lookhind wasn't available when MRE was written):

my $numbers="1 1.0 3.547 123 92.34 343.2234";
while($numbers=~/(?<![\d.])(\d+)(?![\d.])/g){
   print "$1 is an integer\n";
}
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That says: match a bunch of digits that are not preceded by a digit or a dot, and are not followed by a digit or a dot (there be other particular exceptions that I'm not considering at the moment such as grabbing any leading + or - sign if present, but this gives you something to play with).

Update: Ahh, and an important exception I neglected is caught by mirod's version: namely, an integer could occur at the end of a sentence and be legitimately followed by a dot, thus we may want to allow for a trailing dot as long as it isn't followed by digits by changing the negative look-ahead above to the one mirod uses: (?!\d*\.\d).

Here is my take (my takes actually):

#!/bin/perl -w
use strict;
my $numbers="1 1.0 3.547 92.34 12 .25 23.00 23.01 343.2234";

# I guess that's what you were looking for
while($numbers=~/(?<![\.\d]) # first no digits or .
                 (\d+)       # digits
                 (?!\d*\.\d) # then no digits, . and digits
                /gx)
  { print "$1 is an integer\n"; }

print '-' x 20, "\n";

# the same thing slightly simpler
while($numbers=~/(?:\A|[^\d\.])  # catches the character before a numb
+er or the start of the string
                 (\d+)           # digits
                 (?!\d*\.\d)     # then no digits, . and digits
                /gx)
  { print "$1 is an integer\n"; }
  
# much simpler I think
while($numbers=~/([\d\.]+)/g)         # catch all numbers   
  { if( $1=~ /^(\d+)$/)               # keep only integer ones
      { print "$1 is an integer\n"; } # this $1 from the if regexp
  }
  print '-' x 20, "\n";

# now maybe 1.0 is considered an integer
while($numbers=~/(\d+(?:\.(\d+))?)/g)
  { my $nb= $1;                                              # get all
+ numbers
    print "$nb is an integer\n" if( !$2 || ($2=~ /^0+$/) );  # keep th
+ose with no decimal parts 
                                                             # or with
+ a deciaml part only made of 0's
   }
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gives:

1 is an integer
12 is an integer
--------------------
1 is an integer
12 is an integer
--------------------
1 is an integer
12 is an integer
--------------------
1 is an integer
1.0 is an integer
12 is an integer
25 is an integer
23.00 is an integer
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   my $numbers="1 1.0 3.547 92.34 343.2234";

   while($numbers =~ /(^|[^.\d])(\d+)/g) {
     print "$2 is an integer\n";
   }
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   1 is an integer
   1 is an integer
   3 is an integer
   92 is an integer
   343 is an integer
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$_ = "1 1.0 3.547 92.34 343.2234";

while (/(?<![\d.])((?>\d+))(?!\.\d)/g) {
  print "$1\n";
}
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If you want, like mirod did, to match 1.0 as an integer, you would change this to:

/(?<![\d.])((?>\d+(?:\.0+)?))(?!\.\d)/g
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