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Monday, January 15, 2018

Thoughts on infinite depth

Correct mathematics will check out correct over infinity. There is no error or possibility for error. And that is a perfect test. I like to call it--infinite depth. As incorrect mathematics on the surface can look ok, but will lead to contradiction.

Questions of whether or not mathematics can have rules that lead to contradiction were handled most famously with the work of Kurt Gödel being of signature importance. Lots of people talk him, but the essence of the desire with mathematics is what I stated.

People can though get excited over the question of: can you have valid mathematics which leads to something wrong? And I'd say simply: no.

But I see it as, if mathematics leads to something wrong, then is NOT valid. So that idea of a check possible, to me answers the question.

But how can you know? We can't check infinity with infinite tests one-by-one. Where I rely much on tautologies for my work.

Like: x+y+vz = 0(mod x+y+vz) is logically a tautology and mathematically is called an identity.

Is equivalent to: x+y+vz = x+y+vz

Much of my mathematical research reduces back to validity if that identity is valid.

Actually have a reference post from 2014 that is demonstrative:
Example, showing truth, logic and absolute proof

Identities by definition are valid; therefore, a result that so reduces is perfectly checked.

Functionally that means that a person like myself can make a mathematical statement, and find that statement implies something else. Where readily admit have come across such or had them brought to my attention and even when I know have a mathematical proof can be that emotion of FEAR.

Then test the implication and look at a new result. Discovery rules. Fear turns then to elation. But regardless, emotion is irrelevant. The math behaves perfectly. Infinite depth means there can be no mistake. And I marvel to myself or chatter a bit about it, like maybe here on this blog.

So have given the logic. Emotion can mean something else. One phrase like to use, over and over again is--math and emotion do NOT go well together. Like one way I check people is to ask, if they say absolutes do not exist, if they believe: 2+2 = 4

Number authority is so useful. With questions of truth can still be of interest to ask a person, why do you so believe? Most people will of course not debate you over such a thing, but why not?

Simple enough, yes, but there are humans who will debate you over it. I find it to be a telling human check.


James Harris

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