Re: Lowercase equivalent to uppercase, or vice versa


"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.


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.

- Oliver

.

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