# 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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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.

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