# New definitions to the continuum and the discreteness concepts

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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HallsofIvy
Homework Helper

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.