Received-SPF: pass (google.com: domain of jjllambias@gmail.com designates 2607:f8b0:400c:c03::233 as permitted sender) client-ip=2607:f8b0:400c:c03::233;
MIME-Version: 1.0
In-Reply-To: <CAOQ8VDXdv7C7q9E1bau-5A+MV7+ZU_TeRGE6=KOT9=dndU7kmw@mail.gmail.com>
References: <CAOQ8VDUgXJ0iTAO4Vvz+4TbX29tfZbcfptvexaSTJX_StmX85w@mail.gmail.com>
	<CAO7tK2eUKJQe9fsDHgD+rYhDFnyuPpNvQ=A9M7AZHNQt3J6fUw@mail.gmail.com>
	<CAOQ8VDXdv7C7q9E1bau-5A+MV7+ZU_TeRGE6=KOT9=dndU7kmw@mail.gmail.com>
Date: Sun, 17 Aug 2014 12:48:17 -0300
Message-ID: <CAO7tK2dvDDtW_vua10uyT9RvqUENSv=P8TSJapNXaq60gqRLzQ@mail.gmail.com>
Subject: Re: [lojban] A recursively-defined predicate for building chains
 (was: Lojban for great-great-grandfather)
From: =?UTF-8?Q?Jorge_Llamb=C3=ADas?= <jjllambias@gmail.com>
To: lojban@googlegroups.com
Reply-To: lojban@googlegroups.com
Precedence: list
Mailing-list: list lojban@googlegroups.com; contact lojban+owners@googlegroups.com
Sender: lojban@googlegroups.com
Content-Type: multipart/alternative; boundary=001a11c359a0d91fef0500d52ecd
X-Spam_score: -1.9
X-Spam_score_int: -18
X-Spam_bar: -

--001a11c359a0d91fef0500d52ecd
Content-Type: text/plain; charset=UTF-8

On Sun, Aug 17, 2014 at 11:14 AM, Jacob Errington <nictytan@gmail.com>
wrote:

> I can't say that I like using tenfa like this. It seems to me like a happy
> coincidence that we use exponentiation notation for both repeated
> multiplication and repeated function application in general.
>
It's more than a happy coincidence though, it's a natural generalization.
They are both examples of algebraic structures in which exponentiation can
be defined: http://en.wikipedia.org/wiki/Exponentiation#Generalizations

> I also don't like allowing both numbers and predicates in the tenfa, if we
> were to try generalizing it without adding a place for the predicate (in
> which case we pretty much wind up with my predicate, but with the
> possibility of non-natural exponents, which doesn't make a lot of sense
> outside of exponentiation.)
>
> tenfa1 has to be of the same type as tenfa2. You need there to be a binary
operation defined on objects of this type that returns another object of
the same type.

mu'o mi'e xorxes

-- 
You received this message because you are subscribed to the Google Groups "lojban" group.
To unsubscribe from this group and stop receiving emails from it, send an email to lojban+unsubscribe@googlegroups.com.
To post to this group, send email to lojban@googlegroups.com.
Visit this group at http://groups.google.com/group/lojban.
For more options, visit https://groups.google.com/d/optout.

--001a11c359a0d91fef0500d52ecd
Content-Type: text/html; charset=UTF-8
Content-Transfer-Encoding: quoted-printable

<div dir=3D"ltr"><div class=3D"gmail_extra"><br><div class=3D"gmail_quote">=
On Sun, Aug 17, 2014 at 11:14 AM, Jacob Errington <span dir=3D"ltr">&lt;<a =
href=3D"mailto:nictytan@gmail.com" target=3D"_blank">nictytan@gmail.com</a>=
&gt;</span> wrote:<br>
<blockquote class=3D"gmail_quote" style=3D"margin:0px 0px 0px 0.8ex;border-=
left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;p=
adding-left:1ex"><div class=3D""><p dir=3D"ltr">I can&#39;t say that I like=
 using tenfa like this. It seems to me like a happy coincidence that we use=
 exponentiation notation for both repeated multiplication and repeated func=
tion application in general.</p>
</div></blockquote><div>It&#39;s more than a happy coincidence though, it&#=
39;s a natural generalization. They are both examples of algebraic structur=
es in which exponentiation can be defined: <a href=3D"http://en.wikipedia.o=
rg/wiki/Exponentiation#Generalizations">http://en.wikipedia.org/wiki/Expone=
ntiation#Generalizations</a></div>
<blockquote class=3D"gmail_quote" style=3D"margin:0px 0px 0px 0.8ex;border-=
left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;p=
adding-left:1ex"><div class=3D""><p dir=3D"ltr">I also don&#39;t like allow=
ing both numbers and predicates in the tenfa, if we were to try generalizin=
g it without adding a place for the predicate (in which case we pretty much=
 wind up with my predicate, but with the possibility of non-natural exponen=
ts, which doesn&#39;t make a lot of sense outside of exponentiation.)<br>
</p></div><div class=3D""><div class=3D"h5">

<p></p></div></div></blockquote></div>tenfa1 has to be of the same type as =
tenfa2. You need there to be a binary operation defined on objects of this =
type that returns another object of the same type.</div><div class=3D"gmail=
_extra">
<br></div><div class=3D"gmail_extra">mu&#39;o mi&#39;e xorxes</div><div cla=
ss=3D"gmail_extra"><br></div></div>

<p></p>

-- <br />
You received this message because you are subscribed to the Google Groups &=
quot;lojban&quot; group.<br />
To unsubscribe from this group and stop receiving emails from it, send an e=
mail to <a href=3D"mailto:lojban+unsubscribe@googlegroups.com">lojban+unsub=
scribe@googlegroups.com</a>.<br />
To post to this group, send email to <a href=3D"mailto:lojban@googlegroups.=
com">lojban@googlegroups.com</a>.<br />
Visit this group at <a href=3D"http://groups.google.com/group/lojban">http:=
//groups.google.com/group/lojban</a>.<br />
For more options, visit <a href=3D"https://groups.google.com/d/optout">http=
s://groups.google.com/d/optout</a>.<br />

--001a11c359a0d91fef0500d52ecd--