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

On Mon, 02 Apr 2007 12:30:31 GMT, Gordon Sande wrote:
On 2007-04-01 23:38:57 -0300, pa@xxxxxxxxxxxxxxxxxxxxx (Pierre Asselin) said:

Gordon Sande <g.sande@xxxxxxxxxxxxxxxx> wrote:
On 2007-03-30 23:37:53 -0300, pa@xxxxxxxxxxxxxxxxxxxxx (Pierre Asselin) said:
Gordon Sande <g.sande@xxxxxxxxxxxxxxxx> wrote:
On 2007-03-29 18:59:37 -0300, "Lane Straatman" <invalid@xxxxxxxxxxx> said:
[ Paul Cohen's obituary ]

The most
interesting aspect of the seminar was his observation that within six
months of the announcement of his work the set theory technicians had
so advanced the use of his notions that he could no longer read that
literature. His summary was that he was an outsider who had made a
detour into set theory and he was fully intending to get back to real
mathematics. He suggested that the Riemann Hypothesis looked interesting
as a problem. He was a good speaker so the last suggestion may have been
playing to (or with) the audience.

Fascinating. His methods revolutionized the field and are at least as
important as the theorems he proved. I always assumed that he kept up
with the field he opened up.

It was clear from the seminar that the proof technique was of far greater
interest than the actual result. But that is almost a definition of truely
interesting mathematics. I have no idea what he did later although it is a
safe bet that it was interesting.

The axiom of choice and the continuum hypothesis mean different things.

(If X_0 (Aleph nought) is the cardinality of the integers and X_1 =
2 ^ X_0 (cardinality of the power set of the integers) and C is the
cardinality of the reals then the continuum hypotheis is that C = X_1.

No, no. The cardinal 2^X_0 is equal to C and is strictly greater
than X_0, that was known since Cantor. X_1 is the smallest cardinal
greater than X_0, so X_0 < X_1 <= 2^X_0 = C. The CH is that the
second inequality "<=" is actually an "=".

You seem to be objecting to some fact which was not stated. Perhaps
you object to the notation used without looking at the statement.
Notation has a bad habit of drifting over time. Just try reading
some matrix theory from 1900!

I think you need to read more carefully. If we take X_1 to mean 2 ^ X_0,
as stated in the first sentence, then the last statement amounts to the
incorrect claim that CH says C = 2 ^ X_0.



--
Dave Seaman
Oral Arguments in Mumia Abu-Jamal Case to be heard May 17
U.S. Court of Appeals, Third Circuit
<http://mumia2000.org/>
.

Relevant Pages

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