Re: The modern mathematical concept of infinity is indefensible

On 23 jan, 18:48, Ralf Bader <ba...@xxxxxxxxxx> wrote:
umum...@xxxxxxxxx wrote:
On 22 jan, 18:32, Mitch Harris <maha...@xxxxxxxxx> wrote:
On Jan 22, 8:04 am, Han de Bruijn <Han.deBru...@xxxxxxxxxxxxxx> wrote:

Mitch Harris wrote:
On Jan 21, 3:52 am, Han de Bruijn <Han.deBru...@xxxxxxxxxxxxxx>
wrote:

Mitch Harris wrote:

Maybe you have a problem with phrasing that involves 'infinite set'
and 'exists'. Mathematical existence is not the same
as ...uh...physical or sensory existence.

Mitch

Uh, well .. Some people have been thinking differently about this for
almost half a century. I'm an oldie in this group, as the long living
inhabitants here know, and I'm not going to discuss all this over and
over again. In a nutshell: yes, physical or sensory existence IMO
_is_ somewhat the same as or let's say relevant for mathematical
existence.

Rather than worry aboutinfinity, obviously a difficult subject, what
about something as simple as -negative- numbers? Do they exist? Are
they useful?

Negative numbers arise quite naturally from natural numbers as pairs of
naturals with newly defined equality ("equivalence relation") and basic
operations (addition, substraction, multiplication, etc.) on them.

Sure, that's one very particular way of -representing- negative
numbers. You've given a representation (not circular, not already
involving negative numbers) that is manipulable mechanically and which
follow all the rules of what we think of as negative numbers.

But that's not what I'm asking for. You seem to not like the idea of a
realizedinfinity(I don't particularly know one way or the other).
I'm just trying to do the same for negative numbers within what I
think is your world view. I'm just looking for an -actual- negative
number.

(there are of course -other- representations of negative numbers like
strings of digits with a prepended '-', or two's complement with the
first bit set. Frankly, that brings up the whole problem of
representation altogether, is the number 17 actually being used when
you have the digit string '17', or the bit pattern '10001' or even the
tally notation '1111111111111111').

Do you see where I'm going with this?

This is entirely different from howinfinityis introduced.

I don't see how they are different. We can work with representations
('-a + a = 0', 'oo + 1 = oo', or we can work with the ideas
(negatives, where a number plus its negative is zero, orinfinity,
where adding 1 toinfinityresults ininfinity). I don't think one can
show a physicalinfinityand I think that's what you're saying (on the
other hand I think -I- can) but I also think you can similarly not do
it for negatives. (hm...I think I can do that too)

It's freezing: minus 9 degrees centigrade. Right ?

Wrong. Bad temperature scale.

Suppose you have minus 500 Euro on your bank account ?

Han de Bruijn
.

Relevant Pages
Loading