It's not so much the mathematical notation. I have found, in the unusual company I keep, that we utilize the concept of a number that takes any finite positive real (or rational) value, but which is only of interest when it is arbitrarily small. It feels like I might have use for a PA which embodies this concept.--
2011/4/19 djandus <jandew@gmail.com>Isn't this just an option of where to put description? You can use
{ge'o.ebu}, and then describe it as positive, arbitrary, then state at
the end of the proof (as is standard) that it approaches zero. It
doesn't have to be in the name, which is part of the beauty of the
proof -- it never matters that you are sending any variable to zero
until the very end of the proof. That's just a matter of preference,
though. You could have any number of names that could imply any of
what is to come, be it a name for arbitrary variable versus controlled
variables, positive versus negative, or numbers that are going to be
sent to any particular value (possibly a subset of controlled
variables).
On that note, it would be very important /not/ to name epsilon as a
number going to zero, unless the name means explicitly "by the end of
this proof, this variable will be sent to zero by something (not
necessarily me)". If it means "I am sending this variable to zero",
then you are being inaccurate - epsilon is arbitrary, delta we send to
zero, then we prove that sending delta to zero forces epsilon to zero.
It /must/ be a mechanic of the proof that causes it.
A side note: I happen to be saying this from a purely mathematical
perspective, without having studied what Lojban already has available
for mathematical notation.
> 2011/4/19 Jonathan Jones <eyeo...@gmail.com>:
On Apr 19, 3:20 am, james riley <jimr1...@gmail.com> wrote:
> Strictly speaking, in epsilon-delta analysis, epsilon and delta are
> any positive real. We only get interested in them as they get small.
>
> :)
>
> Cmacis
>
>
>
>
>
>
>
>
> > On Mon, Apr 18, 2011 at 8:02 PM, Pierre Abbat <p...@phma.optus.nu> wrote:
>
> >> On Monday 18 April 2011 20:09:21 Ian Johnson wrote:
> >> > For the latter, what's wrong with just using {.ebu} or something, minus
> >> > the
> >> > irritating conflict between this name and Euler's constant?
>
> >> Euler's constant is called {te'o}. No conflict.
>
> >> Pierre
>
> >> --
> >> I believe in Yellow when I'm in Sweden and in Black when I'm in Wales.
>
> > It does conflict with the variable "e", however. There's {ge'o.ebu}, which
> > /is/ "ε".
>
> > --
> > mu'o mi'e .aionys.
>
> > .i.a'o.e'e ko cmima le bende pe lo pilno be denpa bu .i doi.luk. mi patfu do
> > zo'o
> > (Come to the Dot Side! Luke, I am your father. :D )
>
> > --
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Alex R