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

<blmblm@xxxxxxxxxxxxx> wrote in message
news:5706nbF2bea5tU1@xxxxxxxxxxxxxxxxxxxxx
In article <q6mdnVci2skFTpfbnZ2dnUVZ_gydnZ2d@xxxxxxxxxxx>,
Lane Straatman <invalid@xxxxxxxxxxx> wrote:
<blmblm@xxxxxxxxxxxxx> wrote in message
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.

How do you know it's transcendental? I'm willing to agree that it
might be, but can you point me to some evidence other than what you
gave above?
I'm working on that. I think that Lindemann-Weierstrass is going to
work.

After a quick Google search .... I'd have to think and review some
things to understand the theorem. So maybe all along the problem
has been that you are talking over my head. (If it helps -- I have
an undergrad degree in math from many years ago and now work in
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?
OK - was wäre, wenn nicht? Dann ist b algebraisch. Gemäß
Lindemann-Weierstraß ist dann aber tan(b) transzendent. Widerspruch! da ja
tan(b) = a *rational* ist, also sicherlich nicht transzendent. Damit konnte
also b nicht algebraisch sein, sondern muss transzendent sein. Q.E.D.
a=0 ist eine Ausnahme. Dann ist nämlich b = arctan(0)= 0, also ist b
*nicht* transzendent. Thanks to Thomas Nordhaus.

properties,
you're gonna lose commutativity as well. Your implication, my
reductio.
"Your implication, my reductio," is how people agree to disagree. Odd
that
you've never heard it.
(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.
--
LS

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