Re: Why float is called as 'float', not 'real'?



In article <Z_SdnUSLyeNXq5HbnZ2dnUVZ_qarnZ2d@xxxxxxxxxxx>,
Lane Straatman <invalid@xxxxxxxxxxx> wrote:

<blmblm@xxxxxxxxxxxxx> wrote in message
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In article <q6mdnVci2skFTpfbnZ2dnUVZ_gydnZ2d@xxxxxxxxxxx>,
Lane Straatman <invalid@xxxxxxxxxxx> wrote:
<blmblm@xxxxxxxxxxxxx> wrote in message
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In article <I56dnWZ7dZnD7pTbnZ2dnUVZ_sapnZ2d@xxxxxxxxxxx>,
Lane Straatman <invalid@xxxxxxxxxxx> wrote:

Almost all real numbers are not algebraic, and I believe a sure-fire
way
to
find some is taking the arctan of a rational. Consider one-third,
which
could very well look like this:
00111110101010101010101010101011
Do you see a pattern here?

No. Not meaning to be snide, but -- so what?
1010101010101010101010101
Your powers of observation fail you. Look again.

Perhaps we mean different things by "pattern". I took your question
to mean something in the nature of "given the bits so far, can you
easily predict [ based on a pattern you observe ] what the next bits
should be?" I can't, based on the bits you gave, despite the sequence
of repeats of "10" in the middle. Perhaps there's something else I'm
not noticing, or something else that's significant about that repeated
sequence in the middle. Please explain.

Transcendental numbers have a different texture than rationals.

I'm no closer to understanding than I was -- what does "a different
texture" mean in context, and how should it have been apparent from
the bits you quoted, which as far as I can tell still have only
a hypothetical relationship to the value of arctan(1/3).

Well. There are several possible explanations why something you
wrote might not make sense to me -- the reasoning is faulty, the
explication is too terse, I lack the background, perhaps something
else. I initially assumed the first one and attributed it to a
lack of background. Apparently this was far off the mark, and
I apologize for what was probably talking down to you. I'd be
interested in hearing whether other readers were also confused,
if anyone cares to comment.

[ snip ]

I've got a proof. It's in the world's second most important scientific
language:
Jetzt die Voraussetzung a rational. Deine Frage: Muss b transzendent sein?

[ snip ]

Should be of interest to readers who know more German than I do (a
non-zero, but very small, quantity -- but those high-school classes
were a long time ago).

If you make bad scenarios the way you decide about mathematical
properties,
you're gonna lose commutativity as well. Your implication, my
reductio.

[ snip ]

But my "I have no idea what you mean" applied to the whole paragraph.
Most hold mathematical logic to be tautologous. There are, however, often
disagreements among logicians. There aren't any logicians sharper than Paul
Cohen, who died last week. From his obit: "Cohen shocked the math
establishment by proving that the Continuum Hypothesis could not be decided.
The notion that conventional mathematics couldn't prove or disprove concrete
and well known assertions caused an uproar among academics." May he rest in
peace.

Again, this does not advance my understanding of what you wrote.
Thanks for trying, I guess. I'm not really even sure I'm parsing
your sentence correctly -- I can't decide whether you mean "if you
make bad scenarios in the same way you decide about mathematical
properties" or "if you make bad scenarios with regard to the way
you decide about mathematical properties" or something else, or
what.

One more thing and then I'll shut up: It puzzles me that you
find "your implication, my reductio" completely commonplace,
and yet I can't find it with Google. Is it at all possible that
this is a translation from some other language, in which it *is*
a commonplace expression?

--
B. L. Massingill
ObDisclaimer: I don't speak for my employers; they return the favor.
.