New definitions to the continuum and the discreteness concepts

In summary, p and q are real numbers and different notations exist for defining sets of numbers between p and q. A single-simultaneous-connection is a single real number included in p and q, while a double-simultaneous-connection is a connection between any two real numbers in p and q. These concepts are used to define the operation of XOR in mathematics.
  • #1
Doron Shadmi
p and q are real numbers.


If p < q then

[p,q] = {x : p <= x <= q} or
(p,q] = {x : p < x <= q} or
[p,q) = {x : p <= x < q} or
(p,q) = {x : p < x < q} .


A single-simultaneous-connection is any single real number included in p,q
( = D = Discreteness = a localized element = {.} ).

Double-simultaneous-connection is a connection between any two real numbers
included in p,q ( = C = Continuum = a non-localized element = {.___.} ).


Therefore, x is . XOR .___.


Please tell me what do you think ?
 
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  • #2
Okay, you asked:

The first point I would make is that your very first statement:

If p is not equal to q then

[p,q] = {x : p <= x <= q} or
(p,q] = {x : p < x <= q} or
[p,q) = {x : p <= x < q} or
(p,q) = {x : p < x < q} .

is not true. It's only true if p<q and you only said "p is not equal to q".

It's a minor point but symptomatic of your tendency to say things sloppily and without precision. All you are really doing is using big words in non-standard ways without bothering to give precise definitions.

Basically, you do not understand what mathematics IS, and, in particular, the difference between mathematics and physics.
 
  • #3
Hi HallsofIvy,

Thank you for your correction, I am learning from you "on the fly" therefore
I am going to fix my definition and write p>q instead of "p is not equal to q".

Now, after I fix it, please show me by using a formal mathematical way, why my definitions to . XOR ___ are not precise.

Thank you.

Doeon
 

1. What is the continuum concept?

The continuum concept refers to the idea that there are no distinct boundaries or gaps between different values or states. It suggests that everything is connected and exists on a continuous spectrum.

2. What is the discreteness concept?

The discreteness concept is the opposite of the continuum concept. It proposes that there are distinct and separate values or states, with clear boundaries between them. This concept is often used in mathematics and physics to describe discrete or individual units.

3. How do these concepts relate to each other?

The continuum and discreteness concepts are two different ways of understanding the nature of reality. They can be seen as two ends of a spectrum, with most things falling somewhere in between. While the continuum concept emphasizes connectedness and gradual change, the discreteness concept focuses on distinctness and discrete units.

4. Why are new definitions needed for these concepts?

As our understanding of the world evolves, it is necessary to revisit and refine our definitions of important concepts. This is especially true for abstract concepts like the continuum and discreteness, which are constantly being explored and debated in various fields of study.

5. How might these new definitions impact scientific research and understanding?

New definitions for the continuum and discreteness concepts could potentially lead to new perspectives and approaches in scientific research. They may also help to bridge gaps and reconcile conflicting theories, leading to a deeper understanding of the fundamental nature of reality.

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