On Fri, 20 Oct 2006 09:22:50 +0100, steve auvache
wrote:

Ace wrote

[1] Yes, it's really been that long since mathematicians have
theorised about larger and smaller values of infinity.

I dunno. I heard some programme the other day where they were talking
about advances in making rational use of whole sets of infinities to do
modern sums with and how some really interesting work was being done on
it all right now. It had a professor on it and everything so it must
have been good.

A guy called Cantor started[1] the ball rolling back in the 1880s with
his idea of bigger and bigger sets of infinities, which he started to
refer to as 'transfinite' numbers. Lots of clever maths became
possible using them.

Apparently.

[1] For relative values of 'start'.
--
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Ace wrote
On Fri, 20 Oct 2006 09:22:50 +0100, steve auvache
wrote:

Ace wrote

[1] Yes, it's really been that long since mathematicians have
theorised about larger and smaller values of infinity.

I dunno. I heard some programme the other day where they were talking
about advances in making rational use of whole sets of infinities to do
modern sums with and how some really interesting work was being done on
it all right now. It had a professor on it and everything so it must
have been good.

A guy called Cantor started[1] the ball rolling back in the 1880s with
his idea of bigger and bigger sets of infinities, which he started to
refer to as 'transfinite' numbers. Lots of clever maths became
possible using them.

From what I understood and that sort of ended three seconds beyond "good
evening"[1], they have proved recently that there is actually an
infinite number of infinities. Which, it turns out, is a A Good Thing
cos if there weren't the sums would be impossible but as it is they are
now only downright hard.


Apparently.

Indeed.


[1] BBC World Service and Radio 4 have been absolutely cracking lately
for the input hungry. They have been profiling the particular areas of
interest of the various Noble Prize winners rather than the winners
themselves. Very informative it has been. Some awfully harrowing ****
about what is going down in Africa though.
--
steve auvache
i rate dates

steve auvache wrote
Ace wrote
On Fri, 20 Oct 2006 09:22:50 +0100, steve auvache
wrote:

Ace wrote

[1] Yes, it's really been that long since mathematicians have
theorised about larger and smaller values of infinity.

I dunno. I heard some programme the other day where they were talking
about advances in making rational use of whole sets of infinities to do
modern sums with and how some really interesting work was being done on
it all right now. It had a professor on it and everything so it must
have been good.

A guy called Cantor started[1] the ball rolling back in the 1880s with
his idea of bigger and bigger sets of infinities, which he started to
refer to as 'transfinite' numbers. Lots of clever maths became
possible using them.

From what I understood and that sort of ended three seconds beyond "good
evening"[1], they have proved recently that there is actually an
infinite number of infinities. Which, it turns out, is a A Good Thing
cos if there weren't the sums would be impossible but as it is they are
now only downright hard.

Actually that isn't quite right. Recalling back a day or two, they
seemed happy enough that there were an infinite number of infinities but
the jury is still out on there being an infinite number of sets of
infinities but the sums seem to imply there is and it suits them to
believe it.


--
steve auvache
i rate dates

Ace wrote:
On Fri, 20 Oct 2006 09:22:50 +0100, steve auvache
wrote:

Ace wrote

[1] Yes, it's really been that long since mathematicians have
theorised about larger and smaller values of infinity.

I dunno. I heard some programme the other day where they were talking
about advances in making rational use of whole sets of infinities to do
modern sums with and how some really interesting work was being done on
it all right now. It had a professor on it and everything so it must
have been good.

A guy called Cantor started[1] the ball rolling back in the 1880s with
his idea of bigger and bigger sets of infinities, which he started to
refer to as 'transfinite' numbers. Lots of clever maths became
possible using them.

I saw him - didn't he used to lecture down on one knee, called everybody
Sonny Boy?

--
Mike H
R1100RS

Clive George wrote:

"Clive George" wrote in message
...
"The Natural Philosopher" wrote in message
...
Clive George wrote:


How many numbers are there between 1 and 2? The maximum is 2,

The maximum is infinite. 1, 1.0000000000000001,1.000000000000002 etc.
etc...

the
minimum is obviously 1,

No. its zero.

There are NO integers between 1 and 2...;-)

Maximum/minimum numbers, not numbers of numbers...

Apols if you were just trying to be funny - sense of humour slightly
disjointed by presence of drivel talking crap...

Oh, I killfiled him.
never see the *******.

Life gets better.
cheers,
clive

"Dave Plowman (News)" wrote in message
...
In article ews.net,
Doctor Drivel wrote:
How many numbers are there between 1 and 2? The maximum is 2, the
minimum is obviously 1, ie non-zero, and as you should know the
answer is an infinite number. Same as for your number of steps
inbetween. cheers, clive

Find out what integer and real numbers are.

The

Will you please eff off as you are a total idiot.

"Ace" wrote in message
...
On Fri, 20 Oct 2006 09:22:50 +0100, steve auvache
wrote:


A guy called Cantor started[1] the ball rolling back in the 1880s with
his idea of bigger and bigger sets of infinities, which he started to
refer to as 'transfinite' numbers. Lots of clever maths became
possible using them.

In my day they were called Aleph.

On Fri, 20 Oct 2006 12:21:07 +0100, "gomez"
wrote:

"Ace" wrote in message
.. .
On Fri, 20 Oct 2006 09:22:50 +0100, steve auvache
wrote:


A guy called Cantor started[1] the ball rolling back in the 1880s with
his idea of bigger and bigger sets of infinities, which he started to
refer to as 'transfinite' numbers. Lots of clever maths became
possible using them.

In my day they were called Aleph.

Alephplex

--
_______
..'_/_|_\_'. Ace (brucedotrogers a.t rochedotcom)
\`\ | /`/ GSX-R1000K3 (slightly broken, currently missing)
`\\ | //' BOTAFOT#3, SbS#2, UKRMMA#13, DFV#8, SKA#2, IBB#10
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`

On 2006-10-20, The Natural Philosopher wrote:
Mike G wrote:
"The Natural Philosopher" wrote in message
...
Guy King wrote:

Nonsense. You can multiply infinity by anything you like (apart from
zero, of course), it just comes out as infinity again. Just a bigger
infinity.

You can multiply it by zero as well.

Yeah, but what would be the point in doing that?
All that calculation for nothing. :-)

Not at all. Infinity times zero can be any number.

Consider: 3/0=infinity.
now (3/0) * 0 is obviously 3, because the zeros cancel out...;-)

Actually no, 3/0 is undefined, and I'm not certain what the
result of (undefined * 0) is. It's probably still undefined
or possibly 0.

But infinity * 0 is still 0, I'm fairly sure.

--
David Taylor

David Taylor wrote:
On 2006-10-20, The Natural Philosopher wrote:
Mike G wrote:
"The Natural Philosopher" wrote in message
...
Guy King wrote:
Nonsense. You can multiply infinity by anything you like (apart from
zero, of course), it just comes out as infinity again. Just a bigger
infinity.

You can multiply it by zero as well.
Yeah, but what would be the point in doing that?
All that calculation for nothing. :-)
Not at all. Infinity times zero can be any number.

Consider: 3/0=infinity.
now (3/0) * 0 is obviously 3, because the zeros cancel out...;-)

Actually no, 3/0 is undefined, and I'm not certain what the
result of (undefined * 0) is. It's probably still undefined
or possibly 0.

But infinity * 0 is still 0, I'm fairly sure.

Not really. Firstly, there was a smiley.

Secondly the sort of sum shown there is in fact the sort of sum that
lies at the heart of the 'calculus of infinitesimals..'

Where you want to calculate the value of e.g Dx/Dy as BOTH tend towards
zero.

Ultimately the tangent o a curve is definable as 0 divided by 0, but it
has a definite value all right...in the limit one says that it 'tends
towards a given value as dx and dy tend towards zero..obviously AT zero
the line is not a line - its a point and there can not be a tangent..but
the maths really says that you can make it as small as you want and it
will get closer and closer to a given value, as long as you never make
it infinitely small..
Except in discontinuous functions that have a divide by zero in them
anyway..like e.g. cotan(theta)..then not only is the function +-
infinity, but so its its derivative, at 0 degrees

The Natural Philosopher wrote:
Dave Plowman (News) wrote:
In article ,
PC Paul wrote:
Dave Plowman (News) wrote:
In article ,
Guy King wrote:
In what way /isn't/ it infinitely variable? There's a limit to the
ratios each end, but as far as I know, no steps inbetween.
That's what I meant - it doesn't go to zero.

Doesn't go up to infinity either.

BUT it can still be infinite steps in between...

But can their be? The maximum ratio is fixed, so surely to have an
infinite number the other has to be 0?


No. There is an infinite set of real numbers between e.g. 1 and
1.00000000000000000001

PYP!
--
ah

Guy King wrote:
The message
from "Dave Plowman (News)" contains these words:

But can their be? The maximum ratio is fixed, so surely to have an
infinite number the other has to be 0?

Any number space can be infinitely subdivided.

Not natural [1] numbers.
--
ah

[1] n = {0,1,2,€¦,nˆ’2,nˆ’1} = {0,1,2,€¦,nˆ’2} ˆª {nˆ’1} = (nˆ’1) ˆª {nˆ’1}