Re: CONWAY VS CANTOR

On Jul 4, 5:04 pm, Proginoskes <CCHeck...@xxxxxxxxx>
wrote:
On Jul 4, 11:16 am, tommy1729 <tommy1...@xxxxxxxxx>
wrote:



In article

<20664566.1183550822847.JavaMail.jaka...@xxxxxxxxxxxxx
forum.org>,
tommy1729 <tommy1...@xxxxxxxxx> wrote:

and john conway disproves cantor with his
surreal
numbers !!!!

Conway himself does not view it that way.

He notes that the addition he defines is not
the
ordinal addition of
Cantor, but does not claim that two different
definitions cannot both
exist. And be useful for different purposes.

--
G. A. Edgar


http://www.math.ohio-state.edu/~edgar/

i know , he doesnt see it that way...

but accidently thats what he has done :-)

some would call that proof bye contradiction if
you accept both... [...]

Others would call it a proof BY contradiction...

But no, there is no contradiction, since the "+"
sign in the equation
omega + a = a + omega is not the same as the "+"
sign in the
inequality
omega + a =/= a + omega.

It is similar to the "vertical bars" notation,
which has (at least)
two different meanings (absolute value and
determinants):

| -1 | = abs(-1) = 1
| -1 | = det([-1]) = -1

and then claiming a contradiction, since this
"shows" that 1 = -1.

(Or the -1 as an exponent vs. -1 as "inverse
function of".)

--- Christopher Heckman

Just two infinities:

1. potential

2. actual


do you consider yourself a controversial guy too ?

are you against cantor too ?
(if so plz vote in threath "vote on cantor")

under the assumption that with potential you mean unbounded and not a random that might or might not be infinity ; i like the idea of potential and actual.

however, id say to potential : limit.

also there is (actual) countable and uncountable infinity.

so that makes at least 3 not just 2.

greets

tommy1729
.

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