Log in

About this Community
For everyone who is intrigued by numers in nature, fractals, and co-incidental numbers.
In fact, any numerical order/phenomena that is just too cool to ignore.
Pick a number...
Dec. 26th, 2006 @ 06:41 pm 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(abstract) objectivity, abstracting from Alfred North Whitehead's metaphysics, where the (perhaps now unfortunately outdated) term 'Superject' means object, to Whitehead, 'eternal object' (a Subject or 'subjective form' being process, I take the other to be the product.)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?
About this Entry
[User Picture Icon]
Date:December 27th, 2006 04:24 am (UTC)
(Permanent Link)
When you have a function between two sets, f: A -> B, f is a surjection (aka surjective function) if the range of f is B, i.e. if for every b in B, there is an a in A such that f(a) = b. A function which is both injective and surjective is then bijective.

I can't find any mathematical definition of superjectivity, although there seems to be a few philosophical definitions (probably something involving a range bigger than the domain, which in more mathematics is considered impossible, or at least poorly defined).
[User Picture Icon]
Date:December 27th, 2006 06:02 am (UTC)
(Permanent Link)
The piss-poor resources on this important subject, the subject of pure of abstract objectivity, is due to the fact, I venture to say, that the general mathematical inclination is to analysis and quantification, neglecting the necessary other side which is quality and integration (synthesis, analogy). This is especially apparent in the superfluous and overwhelming nature of the Absolte infinte, which is the real infinity, the Infinite, un-bounded, not poorly defined. Infinities in the plural are (more than) poorly defined, they are bettwe called "indefinities" for there is only one Infinity, just as there is only one zero, but the infinite differs from zero by being ungraspable, but real and ultimate, rather than zero who is unreal and not even an entity, as it signifies nothing, it is the epitome of meaningless, the Absolute Infinite is Ultimate Reality, what else could it be? By pure self-reference, it is the actual infinitesimal, unity itself, the point of departure which is pure subjectivity, the "negativity within God" (quoting Levinas, refering to the Absolute Value of the Infinite) which is none other than the unit, unity, one-ness of the one, one-self. Leibnitz and others following his way, could not understand the singularity of the infinitesimal since they deal only with variable quantities which they themselves consider ficticious.