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Tue, Dec. 26th, 2006, 06:46 pm
mostconducive: What is Surjectivity? Superjectivity? and Subjectivity, mathematically?

From the Wikipedia page http://en.wikipedia.org/wiki/Surjection I find the definition of Surjection, Surjectivity, Superjectivity but it is in mathematical language I don't understand, all these symbols of 'functions' I don't get.

I take it to be pure or transcendental (abstract) objectivity, abstracting from Alfred North Whitehead's metaphysics, where the (perhaps now unfortunately outdated) term 'Superject' means object, to Whitehead, 'eternal object' (a Subject or 'subjective form' being process, I take the other to be the product.) Is the object, using the term superject, the 'product' as in multiplication?

Superjectivity, or surjectivity seems to me to have a very precise mathematical definition, just like the differences between injectivity and bijectivity, and subjectivity.

My question, precisely put, is whether there is a more precise definition of subjectivity and superjectivity (certainly the one is just as precise as the other) from mathematics?

What is Surjectivity? Superjectivity? and Subjectivity, mathematically?

Mon, Apr. 25th, 2005, 07:02 pm
devitojason: (no subject)

I need some quick help...

I got a presentation on Thursday about how one can use forcing to prove the independence of the continuum hypothesis (the independence from ZFC....)

So, using forcing to prove Con(ZFC) ==> Con(ZFC + ~CH) is pretty easy...

but....

all the proofs I can find of Con(ZFC) ==> Con(ZFC + CH) which use forcing are more complicated than I'd like to get. In fact, all of them I've found are Con(ZFC) ==> Con(ZFC + diamond), which leads to a prove of the consistency of the generalized continuum hypothesis. I don't need a proof of the consistency of GCH, just one of CH, using forcing.

I suppose I could always resort to Godel's method from 1940, it's just that, knowing a method exists using forcing, I'd like to find a way to simplify it.

Thanks

PS, sorry for those of you who are part of several math communities, don't mean to double/triple/quadruple post...

Fri, Mar. 4th, 2005, 11:47 pm
thecontrolfreak: YES!! A Set Theory Community!

I'm glad you created this community. So's I can get my Geek On.

I've been studying a book thats started me at basic T-F logic and works its way through modal, quantificational, definitions, a small section on the Peano Postulates and recursion, and then ending at Set Theory. I'm fascinated by what I've learned so far, which is a very basic understanding of mathematical logic and some amazing definitions pertaining to functions in a Category Theory book I read as far as I could, which was thinking (from what I understood) that the differences lie in defining Unordered Objects and their Relations vs. Ordered Objects and their Relations. Category theory gave me a little more insight into the concept of a "function" as I kept finding no satisfying and thorough definitions.

Anyone know how exactly these theories app's might differ, and how much farther I have to study (Current Level: College Algebra, sadly) to do some Topology? The concept of Hausdorff Spaces (from what I understand so far) seems really exciting..

Tue, Jan. 25th, 2005, 04:56 pm
wetpanda: (no subject)

do any of you have any good suggestions for books on set theory? i'm interested in the subject but lack the information.

in addition: how can one best describe the null set?

Tue, Jan. 25th, 2005, 04:19 pm
nonbeing: fundamental

I've often heard/seen set theory considered the most fundamental branch of mathematics, insofar as most (all?) other mathematical subjects can be described in set-theoretic language.

It doesn't take a very large leap of intuition to see that many academic disciplines other than mathematics could be cast in terms of set theory, given enough time and effort.

Do you believe a functional, philosophical paradigm could be constructed entirely in set-theoretic terms?

Tue, Jan. 25th, 2005, 09:53 am
tldz: interest suggestions

I would suggest adding "continuum hypothesis", "axiom of choice" and something along the lines of "relative consistancy" to the interests list. Also, I'd suggest giving first names (e.g. "Paul Cohen") of the mathematicians you list. Good list, though. And a good summary of what set theory can become.