(what the correct name for this? commutable?).
commutativity involves only one operation. 
$a + $b = $b + $a

[download]
and at least two operands which get "permuted". thus, it is pointless to ask for commutativity of an unary operation.

the problem is, ++ is not surjective.
or can you find a value for $z so that ++ $z is "Aa0"? no, you can't: 
kabel@linux:~> perl
my ($z1, $z2) = qw/ z9 Z9 /;
print ++ $z1, ", ", ++ $z2, $/;
aa0, AA0
kabel@linux:~>

[download]
thus, ++ does not have any reverse mapping at all.
but if we only allow either lower case or upper case (not both mixed), the problem nearly disappears:
++: /\A[A-Z]*[0-9]*\z/ -> /\A[A-Z]*[0-9]*\z/
++: /\A[a-z]*[0-9]*\z/ -> /\A[a-z]*[0-9]*\z/

[download]
a problem is that "0" has no preimage.
or can you find a value for $z so that ++ $z is "0"? no, you can't. ;D

HTH hehe, finally i was able to apply some knowledge of last years mathematics. hopefully, i am correct. :-)

In reply to Re: Re: $a++ allowed by $a-- is not ! why? by kabel
in thread $a++ allowed by $a-- is not ! why? by abhishes

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.