Registered: Nov 2007
I think you need a basic review of the definition of an equivalence class.
for support of deans claim
from sci logic
Actually its legal to talk about a 7 at the end
of the infinity line. Namely because we are
dealing with ordinals and not with cardinals.
A sequence has more to do with an ordinal
than wie a cardinal, as it orders its elements.
Omega denotes the standard ordinal, which
we normally connect with infinite decimal
numbers. What elsiemelsi does, is simple he
puts forward omega+1.
But there are much much more orders and ordinals,
we could even have omega+omega, or omega+mirror(omega),
12... 12... = omega + omega
12... ...12 = omega + mirror(omega)
12... 12... 1 = omega + omega + 1
..... = omega^2
Nothing special. For example Z, the positive and
negative numbers, are easily seen as mirror(omega)+
... -2 -1 0 1 2 ...
But mirror(omega)+omega is not healthy for numbers,
because the get big!
... 3333.3333 ....
Quite a big number, isn't it?
> Actually its legal to talk about a 7 at the end
> of the infinity line. Namely because we are
> dealing with ordinals and not with cardinals.
OK. Now how does one handle
..333.... x .333... ?
In this New Arithmetic(tm) we should get something like
<i> <w+i> <2w>
where 'w' is omega.
Since 1/3 = .333.... the product 1/3 x 1/3 is clearly
not represntable by a fraction (1/9 = .111..... does not
extend past <w>), and therefore the rational numbers is
not closed under this new system.
This is a minor problem, to be sure...but it *is* a problem.
I'm assuming you have a fix.
Last edited by damsell on 02-25-2008 at 02:50 PM
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