Re: Lowercase equivalent to uppercase, or vice versa


"Oliver Wong" <owong@xxxxxxxxxxxxxx> wrote in message
news:S5DUf.3240$K11.1107@xxxxxxxxxxx

"Rick Smith" <ricksmith@xxxxxxx> wrote in message
news:1225q86q8fh8528@xxxxxxxxxxxxxxxxxxxxx

"Oliver Wong" <owong@xxxxxxxxxxxxxx> wrote in message
news:fGAUf.2907$K11.1151@xxxxxxxxxxx
[snip]
Not sure if "equivalence" has some special meaning in COBOL, but in
math, equivalence is a symmetric relationship. So if A is equivalent to
B,
then it is always true that B is equivalent to A.

My dictionary, RHCD, provides the special definition
for "equivalent", when used for Mathematics, as
"capable of being set into one-to-one correspondence"
and, for "one-to-one", "associating with each element
in one set a unique element in a second set".

I believe this is consistent with the definition I was using above.
For
there to exist a one-to-one correspondence between two sets, those two
sets
must be of equal size. (This sometimes leads to surprising results, such
as
the set of even positive numbers is of the same size as the set of all
integers, including the odd and negative ones).


Consider that age 28 is equivalent to adult, but not the
reverse; that is, associating the set of ages with the set
of {baby, child, teenager, adult, senior}.

The set of natural numbers is NOT in a one to one correspondance with
the set {baby, child, teen, adult, senior}, so the term "equivalent" here
is
not being used in the mathematical sense.

Maybe. The clearest description I have found so far
is "asymmetric relation". An asymmetric relation seems
not to be an "equivalence relation", so 'not mathematical
sense' seems about right. Perhaps, logically equivalent then.
(Though Russell is said to have claimed that mathematics
is a branch of logic!)

As to letter case in COBOL, there are some lowercase
letters that may translate to either of two uppercase
letters, depending on context; while uppercase letters
only map to one lowercase letter, that provided in an
annex in the COBOL standard.

If that's the case (and I wouldn't be too surprised if it were), then
"equivalence" is probably the wrong term to describe the mapping.

I am going to do myself a big favor and let WG4/J4
decide that question.



.

Relevant Pages

  • Re: Lowercase equivalent to uppercase, or vice versa
    ... The set of natural numbers is NOT in a one to one correspondance with the set {baby, child, teen, adult, senior}, so the term "equivalent" here is not being used in the mathematical sense. ... letters, depending on context; while uppercase letters ...
    (comp.lang.cobol)
  • Re: Why no TV?
    ... Sea Wasp wrote: ... caused the following letters to be typed in ... I was the last adult in my family (extended out to the first cousins) to get a cellphone, but I have found that having one has proved most useful to me, socially and professionally. ...
    (rec.arts.sf.fandom)
  • Re: Combinatorial Analysis
    ... Consider V and C as any vowel/consonant from the word MATHEMATICS. ... btw. 1st and 2nd Vs ... This can be solved using the 'formula' for distributing r balls into n ... Substitute the actual letters of the words into the Cs and Vs, ...
    (sci.math)
  • Re: Creating functions for Kabbalah
    ... >> that produce meaninfull relationships within the language.. ... write down the letters in ... > number names from 1 to 9 in English adds up to its value. ... If you look at mathematics as a language the same as english it seems ...
    (sci.math)
  • Woody XFree86-4.3 Symbol font problem
    ... Symbol font is all screwed up. ... Lowercase letters are rendered as uppercase letters, ... Robert Knop ...
    (Debian-User)