On 06/12/2012 10:56 PM, John Gilmore wrote:
The term 'bijective' is a fairly old one, the earliest reference I
found in a Mathematical Reviews index was for 1939.. Anyone who has
had a college course in mathematical logic or, yes, set theory is
likely to know or have forgotten its meaning.
It does, however, have a bad reputation because of its use to
intimidate non-mathematicians. The example in Quine's Quiddities
under the topic mathematosis illustrates why.
Still, it is perhaps better than 'roundtrip', which in ordinary use
does not really imply bijective. My wife and I both found that we
were measurably heavier after a recent Boston-Roma-Boston trip.
Additional efforts were required to restore our status quo ante
weights.
you have two mappings between unicode and ebcdic,
you need an injection from ebcdic to unicode,
and a surjection from the image of that injection
which must be the inverse of the injection.
thus both mappings are bijections between their
field and image and inverse to each other.
in fact no one needs mappings, codes, computers at all,
you just take the universal library, i.e. the bit.
field and image of you two mappings of your roundtrip
are different, still, at least almost, applying a regime
may create a projection that preserve your integrities.
you don't become your wife for example or have your
head cut off.
a mapping that exchanges your with your with is
perfectly bijective and even using itself as inverse is so,
but still, you may have a problem when + is interpreted
as - and vice versa, so you also want preservation of
the somewhat implied semantics of a character/person.
have fun
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