Does "iff" make sense in a definition?
in [Math]
|
Prev: stability analysis, routh-hurwitz criterion, jacobi matrix [urgent] (repost)
Next: Verifying Spherical Coordinate Methods?
From: Frederick Williams on 27 Jul 2010 08:30 "G. A. Edgar" wrote: > > In fact, the short word "iff" was INVENTED (I think by J. L. Kelley, or > was it P. R. Halmos?) When I've seen it attributed to anyone, it's been Halmos. (Who is also responsible for the "box" marking the end--or absence--of a proof.) -- I can't go on, I'll go on.
From: Herman Rubin on 27 Jul 2010 12:17 On 2010-07-27, Frederick Williams <frederick.williams2(a)tesco.net> wrote: > "G. A. Edgar" wrote: >> In fact, the short word "iff" was INVENTED (I think by J. L. Kelley, or >> was it P. R. Halmos?) > When I've seen it attributed to anyone, it's been Halmos. (Who is also > responsible for the "box" marking the end--or absence--of a proof.) There is a major problem with "definitions" in mathematics. There can be only one DEFINITION of something, but there can be large numbers of excellent CHARACTERIZATIONS. In a characterization, iff is definitely needed. It is a mistake to call one set of characterizaing properties THE definition. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin(a)stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558
From: Ludovicus on 27 Jul 2010 12:56 On 26 jul, 18:41, Edward Green <spamspamsp...(a)netzero.com> wrote: Does adding "and only if really add something to "if" when we are stating a definition? Does it even make sense? > There are two forms of defining a set: 1.- .... the elements of A are those that (conditions).... 2.- .... one element belongs to A if and only if (conditions).... Example : Prime numbers are those that have exactly two divisors. A number is prime if and only if it have two divisors. Ludovicus
From: spudnik on 27 Jul 2010 14:11 although one is primary, is it ever considered to be a proper divisor? > A number is prime if and only if it have two divisors. --les ducs d'oil! http://tarpley.net/online-books/george-bush-the-unauthorized-biography/chapter-8-the-permian-basin-gang/ --Light, A History! http://wlym.com/~animations/fermat/index.html
From: Fred on 28 Jul 2010 20:48
On Jul 27, 12:17 pm, Herman Rubin <hru...(a)skew.stat.purdue.edu> wrote: > On 2010-07-27, Frederick Williams <frederick.willia...(a)tesco.net> wrote: > > > "G. A. Edgar" wrote: > >> In fact, the short word "iff" was INVENTED (I think by J. L. Kelley, or > >> was it P. R. Halmos?) > > When I've seen it attributed to anyone, it's been Halmos. (Who is also > > responsible for the "box" marking the end--or absence--of a proof.) > > There is a major problem with "definitions" in mathematics. > There can be only one DEFINITION of something, but there > can be large numbers of excellent CHARACTERIZATIONS. > In a characterization, iff is definitely needed. It is > a mistake to call one set of characterizaing properties > THE definition. I agree with this. I would say something perhaps stronger. The phrase "if and only if" or "iff" is supposed to connect two propositions. The statement "A iff B" is either or true or false (I ask my intuitionistic colleagues to forgive me for that one). It makes no sense to use it in a definition, which is something you are making up---you are not claiming that your definition is true. --Fred |