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According to you.It's not trying to get in a urinating contest, what you are saying is blatantly wrong.
According to you.When I called you on it you insisted you were right and tried to defend it with non-sense.
According to you.I asked you to show me how the body of work in several of the major subjects in math are questions of cardinality, you couldn't.
Pass.If you want I can start grabbing specific theorems, and you can try to show me how it's a cardinality question?
I do.I take it from what you said you don't have a formal math background.
According to you.I do. Math isn't just a question of cardinality.
In your opinion, you're right. In my opinion, I'm right. Go figure.So if you wanna drop this that's fine, but like everything else in math opinion doesn't matter and i'm right on this.
You're university trained in at least graduate level mathematics, and you think that math is just a question of cardinality? What university was this!?I do.
No according to you, your argument never even mentioned cardinality, just relations on sets. Didn't they cover the difference in your formal training?According to you.
If you aren't willing to validate your claim, your positive verifiable claim, we're gonna have to pass, since what you are doing is essentially saying i'm right and I won't prove it.pass
It's the University of Mind Your Own Business, TX.You're university trained in at least graduate level mathematics, and you think that math is just a question of cardinality? What university was this!?
I'm saying I won't rise to your aggression.If you aren't willing to validate your claim, your positive verifiable claim, we're gonna have to pass, since what you are doing is essentially saying i'm right and I won't prove it.
So do we know in advance, or can we completely derive a priori, which statements are provable and which aren't? Ie. given the axioms or definitions, then it follows that x, y, x and only x, y, z is provable and a, b, c and only a, b, c is not?
I suppose not, because if it were true there would not be unsolved theorems like Fermat's etc.
Look i'm not trying to be rude, but you have no idea what you're talking about do you? Have you ever taken any courses in any of the subjects I mentioned?
Also being "derived from sets" doesn't mean it's a question of cardinality, it means sets exist. You described relations on sets, not cardinality. Math is not just a question of cardinality - very few things in math are actually questions of cardinality. I know, I've spent extensive amounts of time doing work in the field (math pun). If you want I can go grab a book in any of the subjects I gave you and start pulling out hundreds of theorems that aren't questions of cardinality, and then show the one or two that are.
I just want to say that I appreciate this little flame war that's erupted over mathematics. It's such a nice variation from rehashing the usual flame wars about politics and religion. Maybe after this one's done we can also have one about Zorn's Lemma.
It's not cardinality has a very definite meaning in math. There is no ambiguity of terms in math.Why don't you cite one of each? This may be a problem in semantics, rather than math.
It's not cardinality has a very definite meaning in math. There is no ambiguity of terms in math.
But Sure. From Galois Theory:
Flipped to a random page and got this for is:
If a is a complex number and a is a root of f(x) whose group is G_a, then a is in the minimal square root field if and only if G_a is constructable.
I had to flip through about 20 pages to find a cardinality related theorem, note this isn't even a question of cardinality like Wiccan claims math is, it just uses it:
If F is finite field, then there is a prime p and integer n such that the |F| = p^n
No it's not. If he's being free with cardinality, then he's not talking about math. Words have meaning.
he claims to be a mathematician.
I claimed to be have a formal background in mathematics, under which a formal education in physics lies.post #21
How does that invalidate my point? My claim is that pretty much all mathematics boils down to the cardinality of sets, inasmuch as layers of abstraction take you to higher-level concepts like rings and fields from simpler concepts like numbers, which are themselves defined in terms of the cardinality of sets (0=|{}|, 1=|{0}|=|{{}}|, 2=|{0,1}|=|{{},{{}}}|, etc). This is a well established way of defining integers, and it virtually all mathematicians accept that set theory is, or at least can be used as, the foundation of mathematics. You are aware of ZFC, right?It's not cardinality has a very definite meaning in math. There is no ambiguity of terms in math.
But Sure. From Galois Theory:
Flipped to a random page and got this for is:
If a is a complex number and a is a root of f(x) whose group is G_a, then a is in the minimal square root field if and only if G_a is constructable.
I had to flip through about 20 pages to find a cardinality related theorem, note this isn't even a question of cardinality like Wiccan claims math is, it just uses it:
If F is finite field, then there is a prime p and integer n such that the |F| = p^n
Look i'm really not trying to be rude, but I don't think that physics counts as a formal background in math. Most mathematicians would agree with me whole heartily. Certainly not formal enough to comment on what all of math is about. You most likely haven't even "seen" most major topics in math in a formal setting. I mean most a physics undergrad typically takes at best one semester of algebra, one semester of analysis, and L.A. or Advanced D.E. if they are lucky - that' it for their advanced math. Even at the P.H.D. level, the math you're required to learn isn't that much more advanced than a bachelors in applied math.I claimed to be have a formal background in mathematics, under which a formal education in physics lies.
Yes, i'm very familiar with ZFC, I actually wanted to do my advanced studies in set theory, and would have if anyone in the community really cared about furthering the field. You know this is one of many ways to define the natural numbers right? And by far, it isn't the most useful. You're argument also is like saying all questions of mathematics is a question of grammar, since proofs are written in the descriptive language.How does that invalidate my point? My claim is that pretty much all mathematics boils down to the cardinality of sets, inasmuch as layers of abstraction take you to higher-level concepts like rings and fields from simpler concepts like numbers, which are themselves defined in terms of the cardinality of sets (0=|{}|, 1=|{0}|=|{{}}|, 2=|{0,1}|=|{{},{{}}}|, etc). This is a well established way of defining integers, and it virtually all mathematicians accept that set theory is, or at least can be used as, the foundation of mathematics. You are aware of ZFC, right?
Look i'm really not trying to be rude, but I don't think that physics counts as a formal background in math. Most mathematicians would agree with me whole heartily. Certainly not formal enough to comment on what all of math is about. You most likely haven't even "seen" most major topics in math in a formal setting. I mean most a physics undergrad typically takes at best one semester of algebra, one semester of analysis, and L.A. or Advanced D.E. if they are lucky - that' it for their advanced math. Even at the P.H.D. level, the math you're required to learn isn't that much more advanced than a bachelors in applied math.
Yes, i'm very familiar with ZFC, I actually wanted to do my advanced studies in set theory, and would have if anyone in the community really cared about furthering the field. You know this is one of many ways to define the natural numbers right? And by far, it isn't the most useful. You're argument also is like saying all questions of mathematics is a question of grammar, since proofs are written in the descriptive language.
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