The correct Wiki link for the congruence of integers is here.
https://en.wikipedia.org/wiki/Modular_arithmetic
Instead, you linked the geometric meaning of congruence. But you have not explained what you mean by saying that 2 and 4 are congruent
in the geometric sense. Until you do, you have said nothing.
Eodnhoj7 wrote: ↑Wed Nov 15, 2017 2:13 am
You are also right about the mod x nature to the symbol.
Yes of course. That's the standard default meaning of '≡' in the context of the integers.
Eodnhoj7 wrote: ↑Wed Nov 15, 2017 2:13 am
You are also right about how their are not specific rules saying a symbol cannot be used in a certain way.
Correct. If I define '2' to mean 3 and '5' to mean 12 then 2 + 5 = 15.
However if you are going to change the standard meaning of a symbol or technical term,
you need to provide a clear, unambiguous definition.
Eodnhoj7 wrote: ↑Wed Nov 15, 2017 2:13 am
So if I take your above perspectives and synthesize them the result is the use of "≡" as a symbol for reflection.
But you have yet to provide a clear, unambiguous definition of your use of the word "reflection." Till you do, your exposition is meaningless. It's devoid of meaningful content.
Eodnhoj7 wrote: ↑Wed Nov 15, 2017 2:13 am
Where I went wrong, if it is to be interpreted in such a manner, is that I did not explain my position thoroughly.
Agreed. And I would say I'm being patient in being willing to engage with you, and to repeatedly ask for a clear explanation of your terminology and symbols.
Eodnhoj7 wrote: ↑Wed Nov 15, 2017 2:13 am
But given the nature of this being a dialect, I would hardly count that as a "sin", considering the nature of the dialectic is precisely about that specifically: finding a common bond of definition as a synthesis of axioms.
What is this, Marxist re-education camp? Where did you get this nutty rhetoric? What does this have to do with your unexplained claim that 2 and 4 are congruent in the geometric sense? You seem to be hiding behind obscure philosophical jargon to avoid dealing with the questions I'm raising.
For a brief moment, you correctly realized that you are being unclear. But instead of then making an effort to be more clear, you decided to wander off into philosophical obfuscation.
Eodnhoj7 wrote: ↑Wed Nov 15, 2017 2:13 am
Nothing noone else has not done before me considering that there is no universal definition as to what mathematics is (Mura), whether it is an art or science (Tobies), or even if it is definable at all (Mura) other than “Mathematics is what mathematicians do” (Mura). It is in this respect the continual observation of symmetry maintains a degree of symmetry within itself, specifically through the axiom as dualism of "symmetry" and "asymmetry".
I agree that one may question the philosophical basis of math. But that has nothing to do with your making up your own terminology and symbols, and then repeatedly failing to give coherent explanations of what they mean.
The fact that philosophers are hard pressed to nail down a precise definition of mathematics, in no way justifies your continued refusal to define your terms and symbols.
Eodnhoj7 wrote: ↑Wed Nov 15, 2017 2:13 am
Contrary to popular belief one can hold two different positions at the same time
in different respects. Much of logic is founded on this simple premise. From this simple premise of thesis and antithesis we are better able to synthesize further axioms.
What that has to do with your arbitrary and unexplained redefinitions of common terms like reflection and common symbols like the triple equal sign, I have no idea. And again, thesis and antithesis. Are you arguing from a Marxist perspective? What would be the point of that? You still have to define your terms if you want to communicate mathematical ideas.