ordinality of sets

[Dale]

when does the ordinalty of set leave logical order and begin illogical
disorder or maybe randomness?

and does that differ for infinite sets or a set of one?

why is this on topic for alt.atheism? science depends on both logical
deduction and logical induction philophies

if there are things that are not logical, it might rule out an
abiogenetic creation, earth or cosmo

the only place I have ever observed possible illogic is within living
behavior

is what I percieve as illogic just uncalculated variancy or
uncalculatable randomness?

Dale

[Dale]

As you deliberately chose to write incorrectly,,
you clearly have nothing intelligent to ask.

ad homenim? explain?
Dale

[Dakota]

Post by Dale
when does the ordinalty of set leave logical order and begin illogical
disorder or maybe randomness?

Are you suggesting that there exists logical disorder and illogical order.

Are you using the word 'maybe' as a modifier of the word randomness?

Do you find spell checkers to be illogical?

How about shift keys?

Post by Dale
and does that differ for infinite sets or a set of one?

What possible order might be found in a set of one?

Post by Dale
why is this on topic for alt.atheism? science depends on both logical
deduction and logical induction philophies

What in particular does the lack of a belief in a god or gods have to do
with science?

Post by Dale
if there are things that are not logical, it might rule out an
abiogenetic creation, earth or cosmo

Neither the pencil on my desktop nor my left nostril seem to be capable
of logic. How soon shall I expect the Earth to vanish? Will it begin
with your vanishing from alt.atheism?

Post by Dale
the only place I have ever observed possible illogic is within living
behavior

It's nice to see that you practice introspection.

Post by Dale
is what I percieve as illogic just uncalculated variancy or
uncalculatable randomness?

Did your dealer tell you how long the effects of the mind altering drugs
you've taken will last?

Post by Dale
Dale

[Peter Percival]

Post by Dakota

Post by Dale
and does that differ for infinite sets or a set of one?

What possible order might be found in a set of one?

Well-order and no need for Choice either!

[Dakota]

Post by Peter Percival

Post by Dakota

Post by Dale
and does that differ for infinite sets or a set of one?

What possible order might be found in a set of one?

Well-order and no need for Choice either!

Please explain what you mean by 'well-order' and what choice has to do
with it.

[Peter Percival]

Post by Dakota

Post by Peter Percival

Post by Dakota

Post by Dale
and does that differ for infinite sets or a set of one?

What possible order might be found in a set of one?

Well-order and no need for Choice either!

Please explain what you mean by 'well-order' and what choice has to do
with it.

Among the many orders that a set can have one of the most significant(*)
is called "well-order". To prove that any set can be well-ordered one
needs the axiom of choice or something equivalent to it (i.e. choice is
necessary and sufficient for well-orderability). But it can be
proved--without the use of choice--that a one-element set is well-ordered.

See, if you wish, http://en.wikipedia.org/wiki/Well-order.

(* In logic and mathematics. I know nothing about physics and atheism.)

[Dakota]

Post by Peter Percival

Post by Dakota

Post by Peter Percival

Post by Dakota

Post by Dale
and does that differ for infinite sets or a set of one?

What possible order might be found in a set of one?

Well-order and no need for Choice either!

Please explain what you mean by 'well-order' and what choice has to do
with it.

Among the many orders that a set can have one of the most significant(*)
is called "well-order". To prove that any set can be well-ordered one
needs the axiom of choice or something equivalent to it (i.e. choice is
necessary and sufficient for well-orderability). But it can be
proved--without the use of choice--that a one-element set is well-ordered.
See, if you wish, http://en.wikipedia.org/wiki/Well-order.
(* In logic and mathematics. I know nothing about physics and atheism.)

Thanks. Am I correct in assuming that every one element set is well ordered?

[Peter Percival]

Post by Dakota

Post by Peter Percival

Post by Dakota

Post by Peter Percival

Post by Dakota

Post by Dale
and does that differ for infinite sets or a set of one?

What possible order might be found in a set of one?

Well-order and no need for Choice either!

Please explain what you mean by 'well-order' and what choice has to do
with it.

Among the many orders that a set can have one of the most significant(*)
is called "well-order". To prove that any set can be well-ordered one
needs the axiom of choice or something equivalent to it (i.e. choice is
necessary and sufficient for well-orderability). But it can be
proved--without the use of choice--that a one-element set is
well-ordered.
See, if you wish, http://en.wikipedia.org/wiki/Well-order.
(* In logic and mathematics. I know nothing about physics and atheism.)

Thanks. Am I correct in assuming that every one element set is well ordered?

Yes.

[Dakota]

Post by Dakota

Post by Peter Percival

Post by Dakota

Post by Peter Percival

Post by Dakota

Post by Dale
and does that differ for infinite sets or a set of one?

What possible order might be found in a set of one?

Well-order and no need for Choice either!

Please explain what you mean by 'well-order' and what choice has to do
with it.

Among the many orders that a set can have one of the most significant(*)
is called "well-order". To prove that any set can be well-ordered one
needs the axiom of choice or something equivalent to it (i.e. choice is
necessary and sufficient for well-orderability). But it can be
proved--without the use of choice--that a one-element set is
well-ordered.
See, if you wish, http://en.wikipedia.org/wiki/Well-order.
(* In logic and mathematics. I know nothing about physics and atheism.)

Thanks. Am I correct in assuming that every one element set is well ordered?

Yes.

I'm feeling rather well ordered myself now.

[Dale]

On Tue, 09 Sep 2014 09:57:25 -0400, Shmuel (Seymour J.) Metz

There is no such thing. Order type applies only to ordered sets.

what is the difference between ordered and unordered sets?

I'll look it up on wikipedia but just figured I'd asked too
Dale

[Aatu Koskensilta]

Post by Dale
what is the difference between ordered and unordered sets?

An ordered set is a set equipped with an ordering, that is, a set plus
a binary relation that satisfies these and those conditions (that you
can look up on Wikipedia).

[Dale]

On Thu, 11 Sep 2014 00:00:01 +0300, Aatu Koskensilta

Post by Aatu Koskensilta

Post by Dale
what is the difference between ordered and unordered sets?

An ordered set is a set equipped with an ordering, that is, a set plus
a binary relation that satisfies these and those conditions (that you
can look up on Wikipedia).

I found this helpful

http://en.wikipedia.org/wiki/Ordered_set

it seems to cover variancy issues but I am looking for definition of
random order and the exclusion or inclusion of illogical order from
ordered and random

ordered things are everywhere in nature

random is a description used in quantum mechanics, but not covered in
the above link

illogical only seems to be present in nature in conscious behavior,
not plants or notconscious life

my thought pattern here is that if there is illogical things that are
not order or random, then science cannot explain all nature and the
philosophies of faith should be investigated, not saying there is an
exclusion of materialism, just that materialism and science itself
might be faiths
Dale

[Peter Percival]

Post by Dale
my thought pattern here is that if there is illogical things that are

What is an illogical thing? I understand illogical person, perhaps one
who maintains both a thing and its opposite, or one who wishes that X
were the case but acts to make opposite-of-X the case. Etc. But thing?

Post by Dale
not order or random, then science cannot explain all nature and the
philosophies of faith should be investigated, not saying there is an
exclusion of materialism, just that materialism and science itself
might be faiths
Dale

[Dale]

On Thu, 11 Sep 2014 11:41:39 +0100, Peter Percival

Post by Peter Percival

Post by Dale
my thought pattern here is that if there is illogical things that are

What is an illogical thing? I understand illogical person, perhaps one
who maintains both a thing and its opposite, or one who wishes that X
were the case but acts to make opposite-of-X the case. Etc. But thing?

if materialism is logical, the brain is material, so thoughts that are
part of the brain are material, all logical

is what we think of as illogical behavior just variant or random and
not illogical, or does the illogical exist leaving science and
materialism as faiths in the face of it
Dale

[Shmuel (Seymour J.) Metz]

Post by Dale
if materialism is logical,

What do you mean by "logical"? What are your axioms and rules of
inference for "logical"?

[Dale]

On Thu, 11 Sep 2014 14:23:59 -0400, Shmuel (Seymour J.) Metz

Post by Shmuel (Seymour J.) Metz

Post by Dale
if materialism is logical,

What do you mean by "logical"? What are your axioms and rules of
inference for "logical"?

static logic is something that can be inferred about a set, a "valid"
deduction from the WHOLE, or "valid" induction from THE PIECES, kind
of hard to know what is really "valid" unless you know the whole or
all the pieces

other than static is like an act of logic, and act of something
belonging to a set of logical things

[Dale]

An order as we mean it in this discussion is just comparing things
somehow. Is Alfred more cromulent than Betty? Less cromulent?
Just as cromulent? We can compare things everywhere in nature,
in lots of ways.

this only applies where logic applies

in a set which includes illogical things, or even in a way that can't
be explained because of illogic, some things get fuzzy

[Jim Burns]

[ sci.physics sci.math removed ]

Post by Dale

An order as we mean it in this discussion is just comparing things
somehow. Is Alfred more cromulent than Betty? Less cromulent?
Just as cromulent? We can compare things everywhere in nature,
in lots of ways.

this only applies where logic applies

No, this applies wherever that is what we mean by "order".

You have the freedom to place whatever meaning you choose
(or no meaning at all) on the words you use, even if that makes
what you say unintelligible. However, we have the same freedom
to continue to place the same meaning as we have been.

It seems clear to me now that you are not going to be doing any
communicating here. It is not so clear to me, though possible,
that you never intended to do any communicating.

Post by Dale
in a set which includes illogical things, or even in a way that can't
be explained because of illogic, some things get fuzzy

[Dale]

Post by Jim Burns
It seems clear to me now that you are not going to be doing any
communicating here. It is not so clear to me, though possible,
that you never intended to do any communicating.

I do plan to go over all of the contents of your previous posts

I just have a short attention span

[Jim Burns]

[ sci.physics sci.math removed ]
<unsnip>

Post by Dale

Post by Jim Burns

Post by Dale

An order as we mean it in this discussion is just comparing things
somehow. Is Alfred more cromulent than Betty? Less cromulent?
Just as cromulent? We can compare things everywhere in nature,
in lots of ways.

this only applies where logic applies

No, this applies wherever that is what we mean by "order".
You have the freedom to place whatever meaning you choose
(or no meaning at all) on the words you use, even if that makes
what you say unintelligible. However, we have the same freedom
to continue to place the same meaning as we have been.

</unsnip>

Post by Dale

Post by Jim Burns
It seems clear to me now that you are not going to be doing any
communicating here. It is not so clear to me, though possible,
that you never intended to do any communicating.

I do plan to go over all of the contents of your previous posts
I just have a short attention span

No, it's not about your attention span.
It's not about you only responding to part of my post, so far.

It's about you misrepresenting what others are saying.

It doesn't matter what the reason is that you do that.
You won't be communicating.

When you do things like snip my comment about what "order"
means, as used here, and then talk about going over all
of my post, as though I was complaining about that,
it looks as though you are _intentionally_ misrepresenting
what I said.

Intentional or not, that is what's (not) happening.

[Shmuel (Seymour J.) Metz]

Post by Dale
what is the difference between ordered and unordered sets?

An ordered set is a pair {s,r}, where r is a relation on s. A set
doesn't have any order per se. For any set larger than a single
element, multiple orders are posible, and for infinite sets, orders of
different order type are possible.

[Dale]

On Wed, 10 Sep 2014 17:37:44 -0400, Shmuel (Seymour J.) Metz

Post by Shmuel (Seymour J.) Metz

Post by Dale
what is the difference between ordered and unordered sets?

An ordered set is a pair {s,r}, where r is a relation on s. A set
doesn't have any order per se. For any set larger than a single
element, multiple orders are posible, and for infinite sets, orders of
different order type are possible.

I found this helpful

http://en.wikipedia.org/wiki/Ordered_set

it seems to cover variancy issues but I am looking for definition of
random order and the exclusion or inclusion of illogical order from
ordered and random

ordered things are everywhere in nature

random is a description used in quantum mechanics, but not covered in
the above link

illogical only seems to be present in nature in conscious behavior,
not plants or notconscious life

my thought pattern here is that if there is illogical things that are
not order or random, then science cannot explain all nature and the
philosophies of faith should be investigated, not saying there is an
exclusion of materialism, just that materialism and science itself
might be faiths
Dale

[Shmuel (Seymour J.) Metz]

Post by Dale
the exclusion or inclusion of illogical order

What do you mean by "illogical order" and does it have anything to do
with Mathematics?

[Dale]

On Thu, 11 Sep 2014 09:52:31 -0400, Shmuel (Seymour J.) Metz

Post by Shmuel (Seymour J.) Metz

Post by Dale
the exclusion or inclusion of illogical order

What do you mean by "illogical order" and does it have anything to do
with Mathematics?

I don't really know, that is the thing about illogic, it can't be
fully concieved unless your mind or conscious contains the set of all
illogical things of which to draw on, such a draw seems to me to enter
the realm of the spiritual/gods if anywhere