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<p style="margin-top:0;margin-bottom:0">This will be a little rant, but I completely disagree with you. It annoys me when authors *don't* use "iff" in definitions, and here's why:</p>
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<p style="margin-top:0;margin-bottom:0">P if Q means that Q implies P. But in the case of definitions, it's a fact of an equivalence. We mean P <---> Q, which also is the meaning of "iff". Using only "if" in definitions causes confusion. Consider the following
example: x=0 if f(x)=0. Do we mean this as something we derived, that x=0 implies f(x)=0? Or do we mean it as a definition of the function f, that f is defined to have only one root x=0? Since definitions are implications both ways, one should use "iff" and
not "if".</p>
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<p style="margin-top:0;margin-bottom:0">It all has to do with the fact that natural language is really bad to state mathematical facts in; and non-mathematicians (like engineers) totally fail to see this point because they are not trained in logic or how a
logical statement looks like. </p>
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<div id="divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" style="font-size:11pt" color="#000000"><b>Från:</b> MacOSX-TeX <macosx-tex-bounces@email.esm.psu.edu> för juan tolosa <juantolo@me.com><br>
<b>Skickat:</b> den 21 augusti 2018 05:40<br>
<b>Till:</b> TeX on Mac OS X Mailing List<br>
<b>Ämne:</b> Re: [OS X TeX] Latex symbol for "define equal"</font>
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<div class="PlainText">This is tangential but, since we are at it, what really, really annoys me, is the tendency in some books to define concepts using “if and only if” instead of plain “if”, as in<br>
<br>
Definition. A sequence (a_n) converges to a real number p if and only if for every epsilon > 0 there is an N such that (etc.)<br>
<br>
(Is it my impression, or there is a growing number of such texts? And when did this nonsense begin?)<br>
<br>
One could simply agree that the “if” in definitions is not the same as the “if” in logical statements.
<br>
If one is really fastidious, one could put a statement at the beginning of the book that “if” in definitions can be reworded as, say,<br>
by “(a_n) converges to p” we mean … (etc)<br>
Or simply not use “if” at all in definitions.<br>
What is even more annoying is that when the definition gets really involved, the “if and only if” makes it even worse.<br>
And, invariably, in a really involved definition you will find that the author(s) abandon their own fastidiousness and just use “if.”<br>
Question is, why not do it from the very beginning?<br>
<br>
Juan<br>
<br>
> On Aug 20, 2018, at 7:56 PM, Markus Klyver <markusklyver@hotmail.com> wrote:<br>
> <br>
> Really, there's no standardized notation for it. Just be consistent and use the most aesthetically pleasing and practical notation on your context. Maybe := looks ugly will your fonts. Use an other notation instead.<br>
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