Set Theory and Natural Fibres
Author(s): Scott Douglas Jacobsen
Publication (Outlet/Website): Trusted Clothes (Unpublished)
Publication Date (yyyy/mm/dd): 2016
So, I want to talk little bit about set theory as it relates to things like categorizations and the definitions of fibres. Set theory is an advanced form of abstraction based around the categorization of things into sets, which are contained in supersets. Supersets contain sets contain elements.
The fundamental units of the sets are elements. A set with an element is called an empty set. But this is some of the strange and weird abstract language that is used to describe this discipline, which is one of the most fundamental domains of discourse for pure mathematics, mathematics, and even physics that describes the natural world.
So, let’s run a little bit of a thought experiment and a simple symbol manipulation experiment with respect to set theory and how we define natural fibres. We can take a squiggly bracket for opening, similar to a parenthetical statement, and a closed squiggly bracket, then we can come up with something like this:
{}
If we take a symbol such as x, y, or z, or actual numbers such as one, two, three, and so on and so forth, we can label those elements. As noted earlier, we can then define the set as the composition of the elements. If we take a set A, we can define it as the most fundamental set, which relates all other sets, which is an intersection of all of them because of the nothingness that contains nothing. Something that contains nothing, in this definition, can then, therefore, relate to everything else. (Huh?) And the Empty Set is such a set:
{} or ∅.
In this case of set A, as an empty set or The Empty Set, will be the representation of it, this means that nothing is contained at this moment in time. If we extrapolate to add elements, let’s say the letter x for an unknown variable, and the number 1for a known variable, we can then have three factors now, we have A, the unknown variable x, and the known variable 1.
We have some fundamental concept sin set theory, too. We have the element, the set, the superset, and the known and unknown variables. Elements make up sets and superset. The latter two do not have much discussion, if at all, in the formalized textbooks, but it’s interesting to note that any set can have elements in them and not know what the precise variable is at that moment in time.
It’s a bit like memory, long-term memory. There’s stuff we know that we know, but don’t have the immediate access it. It’s right at the “tip of my tongue” – so to speak. It’s in our mind, but not known. That’s what I mean. You might have inferred another concept. That a set in a superset is another thing, entirely, which is true: the subset. Let’s put the known variable and the unknown variable into the set now. It will look something like this:
{x, 1}
What else is entailed by this? Two other sets are duplicated or implied by this. One is another set B that contains only the unknown variable x. Another is a set that contains only the known variable, 1. So, we have sets A, B, and C.
Note, the empty set, or the set that contains no elements x, is, thus, intersected between set A, B, and C. If we extrapolate this into the definitions of natural fibres, and synthetic or man-made fibres. We can define natural fibres as set B and synthetic or man-made fibres as set C. Something’s missing here. That’s right.
Set A is the superset of sets B and C. Note, set B and set C are new sets with the same title as the ones before in addition to set A as the superset of sets B and C, the new sets. All of the other definitions of fibres would be elements within A. All natural fibre definitions would be elements in set B.
All synthetic or man-made fibres would be elements in set C. For sake of ease, we can label the old sets A-C the sub-a kind and the new sets A-C the sub-b kind – sub simply means that hyphenated letter placed in front of and below the capital letter representing the set:
A = {}
Aa = {x, 1}
Ba = {x}
Ca = {1}
Ab = {natural fibres, synthetic/man-made fibres} = {Bb, Cb}
Bb = {natural fibres}
Cb = {synthetic/man-made fibres}
See, simple, you can do it, too! You can then infer or deduce properly downwards into subsets and elements that are further composed of these. That’s a small introduction to set theory.
If we were to straightforwardly label the sets themselves, we could come out with him something a little bit interesting with regard to the composition of the definitions. We can replace the F4 mentioned unknown acts and the known one with the titles fibres, natural fibres, synthetic or man-made fibres, and so on and so forth.
It would look something like this: acting like a little bit of a phonics but thought experiment to run! Sorry if this is a little bit of a bore, but I think that this is a viable subject and a very important subject matter and of itself to both think about, pursue, and to play around with as an idea, especially with respect to something else as practically important as natural fibres and textiles. Here’s what I came to with all of that!
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In-Sight Publishing by Scott Douglas Jacobsen is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. Based on a work at www.in-sightpublishing.com.
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