Chimp

1. I am a student.

2. I don't know, but I am not a Phd. :banghead:

3. How does Carlitz's theorem relate to physics? Or is it pure mathematics?

Goliath

Thank you.

Well, consider that the person who taught you calculus might not have had a PhD either. And even if they did, you should know (as a student of mathematics) that mathematics is far too vast for a single person to be knowledgeable in all of the branches therein.

It doesn't. The theorem itself (which was published in the Proceedings of the AMS in 1960) started the study of half factorial domains.

Sincerely,

Goliath

The Evil One

The funniest bit of late was this - Set theory is a language. Mathematics is a language. Therefore mathematics is a set.

By that standard, Welsh is a language, Swahili is a language, therefore Welsh is Swahili.

I'm sure the Kenyans will be gratiified to learn this.

Mike Rosoft

Chimp, do not try to teach me about the set theory. I was studying exactly that a year ago.

Now if you use your capacity for abstract thought, like I know you can, you will see that sets are also numbers.

No! Not every set is a number. Sets can be used to represent numbers: empty set represents the number zero, a set containing an empty set represents the number one, a set containing "zero" and "one" (an empty set and a set containing an empty set) represents the number two, etc. But there are many sets which do not represent any number.

If we make a powerset of a set representing a natural number x, we get a set representing the number 2^x. But if we use sets to represent real or complex numbers (and there is nothing to prevent us from doing so), this will no longer be true.

Sets are quantities that contain other sets.

Sets and classes are different things in the set theory.

A class is a compound of all sets for which a particular statement is true. For example, a class of all sets exists. Not every class is a set. (But every set S represents a class; namely, a class of all sets x for which x is an element of S.) Only sets can be elements of a class, not classes which are not sets.

A class of all sets is not a set. (If it were, it would have lead to a self-contradiction.) By definition, a class of all sets does NOT contain itself.


Mike Rosoft

Goliath

Of course it's ridiculous...doubly so, as mathematics contains objects that are not sets.

*sigh* Chimp, if you really are a student of mathematics, then you have a lot to learn.

Sincerely,

Goliath

Chimp

Mathematics is a language, set theory is a language. Sets are ideas.

More oversimplification from the Evil One?

Chimp

The "Universal Set" is defined as an algorithm. No contradiction. :boohoo: for you then.


Here is the definition of "algorithm":

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

[QUOTE]


"Algorithm

From Wikipedia, the free encyclopedia.

Broadly-defined, an algorithm is an interpretable, finite set of
instructions for dealing with contingencies and accomplishing some
task which can be anything that has a recognizable end-state,
end-point, or result for all inputs. (contrast with heuristic).
Algorithms often have steps that repeat (iterate) or require decisions
(logic and comparison) until the task is completed."

[QUOTE]

DNA is an algorithm, a finite set of instructions, which can construct
a carbon based life form.

The life form physically contains the DNA and the DNA contains the
life form in an "abstract" sense.

At a fundamental level of existence, it is postulated that "nature"
could be constructed of tiny strings, and those strings, loops, or
branes, could even be constructed of string "bits".

These bits could encode information, analogous to the universe's
"DNA"? A set of instructions built into the fabric of space/time and
mass/energy?



http://www.blc.arizona.edu/Molecular...TML#Components

AGCT looks like code to me... DNA? = information?

Physicist Stephen Hawking writes:



At the most fundamental length scales, the fundamental paticles,
called "strings", could be constructed of even more basic units i.e.
bits? analogous to a computer code?

1010100010...etc.

Universal algorithms?

This assumption seems to hint for a designed universe, or even
stranger still, a universe that is a type of life form...???



Some interesting ideas on "string bits":

http://xxx.lanl.gov/PS_cache/hep-th/...07/9607183.pdf

http://xxx.lanl.gov/PS_cache/hep-th/...07/9707048.pdf



According to string theory, the uncertainty in position is given by:

Dx < h/Dp + C*Dp

Which points towards a type of "discrete" spacetime?

Interesting...

Mike Rosoft

A set is an algorithm? What on Earth are you talking about?

And, it is irrelevant how you created the "universal set" (which, I assume, is supposed to be a set containing every set). It has absolutely no effect on the proof that the universal set cannot exist.

Edited to add:

And I have no idea what is the relevance of the Wikipedia quotes on "algorithms". Did you even try to follow what I am trying to tell you?


Mike Rosoft

Goliath

Chimp,

Algorithms, I suppose, can be thought of as sets, but sets are not algorithms. "Set" is an undefined term. This means that whenever you try to define "set", you're wrong!

Again, it has been proven that for any set A, there cannot be an onto map from A to 2^A, whence there is no such thing as the set of all sets. Deal with it.

Sincerely,

Goliath

Goliath

Tell me, in your own words what this means, or concede.

Again: in your own words.

Sincerely,

Goliath