Mathematics and logic are the human disciplines which can rely on absolute proof. And I think it interesting to consider the possibility of people who don't even believe that exists. But it is a cool thing which theoretically removes the problem of conflict with mathematical ideas. Or as I like to say, proofs don't fight.
However there can be things subject to interpretation, though functionally I went ahead and presented a method for always determining mathematical proof which can be logically determined to be perfect, which is to begin with a truth, and proceed by logical steps. At each logical step, you have a truth, so my functional idea was to connect truth to truth with logic connectors. Oh, you may wonder, but how do you know you began with a truth? Good question. Um, asking myself and noting.
And I made an example to demonstrate just so can point to it when discussing:
Example post demonstrating absolute proof
Which I think is handy.
The example shows that with the condition that x2 + y2 = z2, then
(v2 - 1)z2 - 2xy = 0(mod x+y+vz) must be true, where v is a free variable.
So, since v is free, let's say I let v=10, then I know that 99z2 - 2xy has x+y+10z as a factor, when x2 + y2 = z2.
Like if x = 3, y = 4, then z = 5, and 99(25) - 2(3)(4) = 2451, and 3 + 4 + 10(5) = 57, and 2451 divided by 57 equals 43.
You get trivial results like that here but can use this approach to probe into LOTS, where v is a tool of your mood. I like that, and in fact picked 'v' for victory, mostly.
That result is absolutely true where those expressions are available, without regard to ring. I like that.
Oh, and I made up that mathematical analysis path, and like to call the mathematical area--modular algebra symbology. For some reason now that naming...well is accurate. Naming things is fun but at times I wonder at my choices. Where use what I call tautological spaces, where advanced the concepts enough to cover all the mathematics interesting to me.
But yeah to me modular algebra symbology is SO cool, and it helps that I made that up, so is my own personal mathematical discipline, but others can use of course but for me will always feel different. And yeah I pioneered a functional approach to determining if you have mathematical proof, so it feels different using it too.
Web search is an AWESOME way to check a person on bold claims. Easy is to just search on modular algebra symbology, as yeah I did make that up. Also you can search on tautological spaces, as I made that up too! While checking me on how people check mathematical proofs is where the hardest work may be, but search on that too where will not suggest searches. If interested, figuring out how to search to check me on functionally defining mathematical proof is useful as well.
Because mathematics can allow absolute proof it does make it kind of boring to argue it, and I quit that years ago, though will admit that the utility of arguing about mathematics is about finding error. So it DOES have value, arguing about mathematics, but in my opinion, the only value is in finding error which means a mathematical argument is NOT proof.
Sure someone can CLAIM absolute proof, but does that same person actually have it?
Turns out I figured out how to check, and yup, do use it! Is fun.
And yes, to me saying absolute proof is redundant but is useful for emphasis and clarity.
Proof lets you move on and do other things, like find more mathematics! Or hang out. Do something entertaining, or some other kind of work. Or, whatever.