Re: abundance of irrationals!)

Dave Rusin said:
> In article <MPG.1ce175f0d96da894989b7e@xxxxxxxxxxxxxxxxxxxxxxxxx>,
> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
>
> >Infinite means "without end", and takes several forms.
>
> Mathematicians use it to mean "not finite", although since it is an
> adjective it only appears in a context like "This is an infinite X" where
> X is a noun; mathematicians might prefer to treat "infinite X" as a
> single noun phrase to be defined, thus never reall defining "infinite"
> at all!
Well you didn't define finite either, so I'm not surprised. I'm trying to help
here. If we can't even agree on our definitions for terms, then how can we use
them in any precise manner?
>
> >All those forms and understandings must be in accord.
>
> Open a dictionary and count the number of definitions for "set".
> They're not all even from the same part of speech, much less being
> in accord.
Forms of infinity. I am beginning to think Cantor also taught people to read
each sentence in isolation. That would certainly help his system considerably.
>
> (We do hope the multiple uses of a single word are more or less similar
> but this is not always the case for historical reasons. If I have a
> closed 1-form on a closed set, there is no connection between the
> two uses of the word "closed". Pity, that.)
Is there an agreed on definition of "infinite" that enables us to know what
each other is talking about?
>
>
>
> >> The word limit tells it also we are always on our way but we are never reaching it.
> > Last I heard a limit was an end, a stopping point.
>
> Informally, perhaps. I'm sure many mathematicians would say they've
> reached their limit with this discussion. But when they're using the
> word "limit" in a mathematical sentence, they have a precise meaning
> for it, which does not involve the terms "end" or "stopping point"
> at all. For example, the (correct) statement
> the limit of f(x) = x sin( 1/x ) as x tends to 0 is 0.
> may be expressed as a cumbersome but precise statement about the
> behaviour of the function f near zero. The words "end" or "stop"
> never occur in the translated statement.
near zero, or at zero? Most limits give pretty precise values for what is
happening at that precise point.

I think mathematicians reach their limits when they see their favorite axioms
crumbling before their eyes. No one has refuted my proofs except by changing
the subject or inserting some external interpretation that is incorrect. I
challenge you to find a flaw in either. Look at my post from 5/3 at 3:57 PM.
>
>
> dave
>

--
Smiles,

Tony
.

Loading