
tWebber
Originally Posted by
mattbballman31
Okay, dummy. Whatever you say. Go get lost!
Gotta love the Christians!
“He felt that his whole life was a kind of dream and he sometimes wondered whose it was and whether they were enjoying it.”  Douglas Adams.

tWebber
Originally Posted by
shunyadragon
I do not spoon feed the intentional ignorant.
Why should I do your job for you?

tWebber
Originally Posted by
Tassman
Gotta love the Christians!
We love you too, Tass Guy the Scientism Guy!
Many and painful are the researches sometimes necessary to be made, for settling points of [this] kind. Pertness and ignorance may ask a question in three lines, which it will cost learning and ingenuity thirty pages to answer. When this is done, the same question shall be triumphantly asked again the next year, as if nothing had ever been written upon the subject.
George Horne

tWebber
Originally Posted by
Chrawnus
Why should I do your job for you?
Your the who asked me to do your laundry. It is your problem that you are not will to read the references and do the homework. At present you have an F.
For example in the course of this thread Boxing Pythagoris does do the homework and responds intelligently to the thread when responding in the dialogue.
Originally Posted by
mattdamore
At this point, I need to use characters for the Greek alphabet, which I don't have. I'll use an English transliteration, but I apologize if this is cause for confusion. I'll try my best to be as clear as I can.
Originally Posted by
Boxing Pythagoris
Most fonts support Greek and Hebrew characters, these days, but you'll have to use some extra manner of accessing them for example, the Charmap program in Windows or
http://typegreek.com/
Another option, and the one which I prefer, is to use LaTeX formatted images. This tool is very helpful in that regard:
http://www.codecogs.com/latex/eqneditor.php
Omega = Aleph null  [Omega is the first infinite ordinal. Aleph null is first infinite cardinal: the set of all natural numbers. The set of all natural numbers is countably infinite.  The sets above this point are all finite.]
It is not quite true that . The cardinality of omega is Aleph null, but ordinals and cardinals are very different sorts of numbers. We can't just equate them in this way. For example, it is true that ; however, we know that . Saying that these two numbers equal one another would make our mathematics inconsistent.
Originally Posted by
mattdamore
As I said, I am a rank amateur when it comes to this concept, and I have probably made mistakes above. Any contribution or clarification is most welcome.
Originally Posted by
Boxing Pythagoris
In general, it is useful to note the difference between ordinal and cardinal numbers. Ordinals, as their name implies, are a description of how elements of a set may be ordered. Cardinals, on the other hand, are a description of how the elements of one set can be mapped onto another. So, ω describes the first number which is ordinally greater than any Natural number, in transfinite arithmetic. On the other hand, represents the cardinality of any set which can be mapped with 1to1 correspondence onto the Natural numbers.
I have consistently followed and agree with Boxing Pythagoris's view of Math concerning infinities/ Where are you at?
Originally Posted by
Boxing Pythagoras
Calculus is a tool for calculating actually infinite sets of objects, and this tool can be used to describe the workings of the real world with incredible accuracy, as Newton demonstrated with his celestial mechanics. There is some philosophical debate, however, as to whether such tools are just decent idealizations which provide reasonable approximations of reality, or whether they accurately describe reality.
I'm a Formalist when it comes to the philosophy of mathematics, so I think ALL mathematics is a purely abstract means of describing the real world including basic arithmetic. However, there are ways in which this abstraction can be more or less accurate in its description of the world.
Actually, doing your own homework can amount to simply reading Boxing Pythagoris's posts.
Last edited by shunyadragon; 03272018 at 12:56 PM.
Glendower: I can call spirits from the vasty deep.
Hotspur: Why, so can I, or so can any man;
But will they come when you do call for them? Shakespeare’s Henry IV, Part 1, Act III:
go with the flow the river knows . . .
Frank
I do not know, therefore everything is in pencil.

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