Sunday, August 11, 2013

Categorical Introduction to Set Theory

Let {} represent a set.

{} is boundless or represents a definition.

By Wittgenstein, definitions are atomical facts. Conceptually, a definition can have any volume, and any shape a definition takes is a formality which seeks justification.

The argument that {} represents more than a point in space is untenable unless a formality is adopted.

{However, a point in space may contain any form of representable information}

Now consider three variables, which are NOT necessarily mathematical:

'{}, info, formality'

[{}] is the form of [formality]

[info] is the contents of the [{}]

[{}] is the observable [formality]

[{}] is the formal definition

There are infinite points in a non-typological line.

If [{}] is finite, it does not take up space, unless that space is typological.

To be an observable formality, the [{}] must be infinite or typological, or both.

However, [info] necessarily has a definition, a necessary bound.

[info] without definition would be an unbounded unbounded [{}], an empty [{}].

[info] must be bounded, while the [{}] must be unbounded.

Essentially, the [{}] must formalize the [info], or the result is an empty [{}].

The obvious answer is that the formality of a [{}] consists of typological [info].

At this point, the missing variable is mathematics.

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