Could null set exist as part of a physical model?

In summary, the conversation discusses the concept of opposites and how they can define and contribute to the understanding of a larger context. It also raises the question of whether the concept of an empty set could be introduced into the description of a larger context, such as in the case of multiple universes. The speaker also mentions the need for precise definitions and boundaries in both language and mathematics in order to fully understand and describe a concept.
  • #1
zankaon
166
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The opposite of a great truth is also a great truth - T. Mann

For example, the opposite of empty set {} is a non-empty set, such as the set of integers, or finite sets we experience in our mundane lifes.

Also a lesser context can define the greater context, and vice versa.That is, each is defined by what it is not i.e. its antithesis; for example, the antithesis of quanta and spacetime manifold.

So what if a physical model such as our universe, or a divergent cyclical set of universes (hence non-empty set with 1:1 correspondence to integers), has a greater context of simplest case i.e. empty set? Might this be indirectly inferred; of course without perturbing such alleged greater context? Such as if there were multiple 'universes'.

So could {} be introduced into consideration of a description of a larger context?
 
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  • #2
I've been contemplating this issue lately-- this is a problem that is *sorta kinda* addressed in the Axiom of Choice and in the theories of Borel, Lebesque and Godel in a big sort of way. The main concern that I have had with this idea is that even a physical model would have to have some sort of set limit-- and I even have problems with this being a conceptual model of mathematics because Cartesian sensual realism cannot cope with such abstractness. I wish that I could get a good grasp on this notion. :/
 
  • #3
zankaon said:
The opposite of a great truth is also a great truth - T. Mann

For example, the opposite of empty set {} is a non-empty set, such as the set of integers, or finite sets we experience in our mundane lifes.

Also a lesser context can define the greater context, and vice versa.That is, each is defined by what it is not i.e. its antithesis; for example, the antithesis of quanta and spacetime manifold.

So what if a physical model such as our universe, or a divergent cyclical set of universes (hence non-empty set with 1:1 correspondence to integers), has a greater context of simplest case i.e. empty set? Might this be indirectly inferred; of course without perturbing such alleged greater context? Such as if there were multiple 'universes'.

So could {} be introduced into consideration of a description of a larger context?

This is just my opinion so take it or leave it.

In any descriptive language in order to define something you need two definitions: the thing you are describing and its complement. If you can't strictly define both of these, then you have not given a clear definition.

When working with sets, the union of a subset and its complement are required to define the "universe" that it exists in.

In this sense in order to describe "everything", you need to define "nothing", just like you would make a definition of "hot" and "not hot" or "black" and "not black".

In saying this if you had to give a description that corresponded to "everything" as a description of some physical phenomena, then there must also be a description of "not everything" and if a mathematical description of "everything" was written in terms of set and its boundaries were precise, then the definition of "not everything" should be precise.

There are probably philosophical arguments about this, but I am not a philosopher: I am looking at this from the point of language since in order to formulate an idea, let alone a model, you have create a descriptive boundary of some sort that describes not only the idea or model, but its complement with respective to the limits of the language used to describe it.
 

What is a null set in a physical model?

A null set, also known as an empty set, is a set that contains no elements. In a physical model, it would represent a situation where there are no objects or entities present.

How is a null set different from a zero set?

A zero set is a set that contains a single element, which is the value of zero. A null set, on the other hand, contains no elements at all. In a physical model, a zero set would represent a situation where there is one object with a value of zero, while a null set would represent a lack of any objects.

Can a null set exist in a physical model?

It is possible for a null set to exist in a physical model, depending on the context and the objects being modeled. However, it is important to note that a null set is an abstract concept and may not always have a physical representation.

What is the purpose of including a null set in a physical model?

In some cases, including a null set in a physical model can help to accurately represent a real-world scenario where there are no objects present. It can also be useful in mathematical and logical operations.

How is a null set represented in a physical model?

In a physical model, a null set can be represented by an empty space or by the absence of any objects. It can also be represented symbolically as the empty set symbol (∅) or by using the word "none" or "empty".

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