Re: Multiple infinities - one more look

On Dec 6, 7:02 pm, Venkat Reddy <vred...@xxxxxxxxx> wrote:

For me, here is how things are. For integer sequences such as 1,2,3,..
and 2,3,4,... there is a possibility that one can always insert a new
number at the end.

Sequences such as 1, 2, 3 ... do not have an end.


Instead of ordered pairs and triplets, if we consider "ordered
infinite" sets, we can still produce a sequence [...]

Some infinite order relations can be mapped to sequences, but
some cannot.


Actually even in the case of ordered pairs (rationals), a single mini
traversal takes infinite number of steps when the numbers in the pairs
hit infinity.

No rational numbers have infinity as numerator or denominator.
(Also, one cannot "hit" infinity. Infinity isn't a position in a
sequence.)


If something is countable, why should be called infinite?

Because it isn't finite?


Doesn't counting fail because there are no
adjacent numbers at infinity
[...]
If there are adjacent numbers at infinity, then adding one
to infinity should produce a new number.

There is no "at" infinity. Infinity is not a position in a sequence.


So I believe infinite is always
uncountable by definition.

You are certainly free to make up your own definitions, however
by the standard definitions, your claim does not hold.

What definition are you using for the terms: sequence, countable,
uncountable?


Marshall
.

Relevant Pages

  • Re: Find out if I/10^i = J/2^j (decadic - dyadic pairing)
    ... 0s with different valency towards infinity; ... "that real number which is the limit of the sequence of rational ... If two different sequences of digits have the same limit in the ... of rationals being the buzzwords). ...
    (sci.math)
  • Re: The Paradox of Zeno
    ... Since eleaticus cannot refute my statements, ... And the definitional "formula" for convergence of a sequence in standard ... analysis does not mention infinity, at least in any of the math texts or ... If one moves one metre in one second and half a metre in the next half ...
    (sci.math)
  • Re: The Paradox of Zeno
    ... Since eleaticus cannot refute my statements, ... And the definitional "formula" for convergence of a sequence in standard ... analysis does not mention infinity, at least in any of the math texts or ... If one moves one metre in one second and half a metre in the next half ...
    (sci.physics)
  • Re: The Paradox of Zeno
    ... Since eleaticus cannot refute my statements, ... And the definitional "formula" for convergence of a sequence in standard ... analysis does not mention infinity, at least in any of the math texts or ... If one moves one metre in one second and half a metre in the next half ...
    (sci.physics.relativity)
  • Re: Cantor and the binary tree
    ... According to Cantor ... > well-ordered and simultaneously ordered set < of all rationals, ... What you are doing is defining some sort of sequence of infinite sets. ... carried away and use sloppy wordings like 'at infinity' or 'after ...
    (sci.math)