[OS X TeX] Latex symbol for "define equal"
"Néstor E. Aguilera"
nestoreaguilera at gmail.com
Tue Aug 21 08:10:57 EDT 2018
Hi everyone:
It seems to me that when we use "=" or another symbol in a "definition" we are actually stablishin a "notation". When we say "A is invertible if/iff/when..." this looks more like a definition, but it is actually a naming convention (right?), that is, a variant of notation, where we use a name to describe a perhaps complex situation.
Knuth "defines" (as stated in Appendix B) the "bracket notation" (ACP, Vol 1, §1.2.3, equation (16)) using "=" and "if".
Perhaps somebody can explain what are the differences, if any, between "definition" and "notation".
Best,
Nestor
===============================================
> On 21 Aug 2018, at 08:49, Markus Klyver <markusklyver at hotmail.com> wrote:
>
> Definitions *are* equivalences.
>
>
> Från: MacOSX-TeX <macosx-tex-bounces at email.esm.psu.edu> för Ross Moore <ross.moore at mq.edu.au>
> Skickat: den 21 augusti 2018 13:21
> Till: TeX on Mac OS X Mailing List
> Kopia: TeX on Mac OS X Mailing List
> Ämne: Re: [OS X TeX] Latex symbol for "define equal"
>
> Hi all.
>
> I agree with using "when", or better "precisely when", in definitions.
> Do not use these words in theorems. There are many alternative ways to express what you want.
>
> But didn't this thread start out asking for a symbolic notation?
> In that context, equivalence is *not* the word you want for a definition, as equivalence depends on a particular relation, so is weaker than a definition.
>
> There are nuances in mathematical concepts and notations that are not always correctly appreciated by those who work primarily in other (mostly applied) fields.
>
>
> On 21/08/2018, at 13:03, "Markus Klyver" <markusklyver at hotmail.com> wrote:
>
>> But how would the reader know if it's a theorem or a definition? Consider the statement "f(x)=1 when x=2". Do we mean f(x)=1 <---> x=2 or just f(x)=1 <--- x=2?
>>
>>
>> Från: MacOSX-TeX <macosx-tex-bounces at email.esm.psu.edu> för Josep Maria Font <jmfont at ub.edu>
>> Skickat: den 21 augusti 2018 12:15
>> Till: TeX on Mac OS X Mailing List
>> Ämne: Re: [OS X TeX] Latex symbol for "define equal"
>>
>> That's why I prefer to use "when" for definitions: [...this NEW thing happens...] WHEN [...such-and-such known, understandable condition holds...].
>>
>>
>> JMaF
>
>
> Cheers,
>
> Ross
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