Bored? Try this math challenge. :)

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GeorgAnatoly wrote:

Thanks for the feedback, I want to make myself as clear as possible.

It is still a poor description of the problem. Try:

Suppose there are two points on a plane, • •. When you draw a line connecting the points, it forms one line segment, •---•.

With three points you can create three line segments: EVNnuU1


Define the relationship between the number of points x and the maximum number of line segments which begin and end on these points (which you choose) : y.

I intentionally phrase the lines turning the points into 'pairs' because it gives a hint as to what the solution is. It makes it kind of obvious that x/2 is part of the solution.

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Disrupted wrote:

Traditional math would say this is impossible. But we can accomplish the impossible if we allow 'x' to be a lambda (aka function).

x-7 = 19+x
x-x = 19+7
x-x = 26

So we have the difference between x and itself is 26. A contradiction if x were a simple number.

But we can make x= -13 AND 13 through a duplicitous function using powers;

x^4 = 13^4

I tried to show this technique to the math reddit a few weeks ago and i got eviscerated for suggesting something new (oh the horror /sarcasm)

You're running into violations of additive inverse/additive identity and the properties of equality when you try to show there is a real number solution to the equation x-x≠0. The proof to your idea that there is a solution, if one exists, wouldn't come in the form of a set of operations on real numbers but rather you would have to prove there are a set of numbers where x-x≠0 is true. And I'm not 100% sure but I think set theory would prevent this. E: Meaning you would probably have to prove there is a non-trivial parallel set of numbers to (((((N)I)Q)R)C).

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GeorgAnatoly wrote:

You're running into violations of additive inverse/additive identity and the properties of equality when you try to show there is a real number solution to the equation x-x≠0. The proof to your idea that there is a solution, if one exists, wouldn't come in the form of a set of operations on real numbers but rather you would have to prove there are a set of numbers where x-x≠0 is true. And I'm not 100% sure but I think set theory would prevent this. E: Meaning you would probably have to prove there is a non-trivial parallel set of numbers to (((((N)I)Q)R)C).

But as i stated, x is not a number. It is an entirely new class of lambda constructs. Thus most of math simply cannot be straightfowardly applied to it. Nor does it need to be 'proven'. There are axioms we simply have to accept in math. I am proposing a new one that applies only to a very narrow subset of problems. It has potential applications where contradictory truths exist, such as in AI or in quantum mechanics.

At a minimum you would have to fully define the set of; 'narrow subset of problems' and 'contradictory truths'. I'd suggest reading something like Naive Set Theory by Halmos if you're really interested in this kind of thing.

Saying "x is not a number" when dealing with algebra delves very deep into trick question territory. And that's giving it more credit than it likely deserves.

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ScrotieMcB wrote:

that's giving it more credit than it likely deserves.

After all this time... and you still cant show respect?

All of math is a construct of the mind. A very advanced construct, sure. But every bit of it was created by man.

It is *mostly* consistent while describing reality. And for good reason, it was designed around it. Had reality been different and it took 2 full revolutions to reorient something being spun, our math would reflect that instead of what we have now. (btw, there is such a thing as a spin 2 particle in physics that is precisely what i described).

To think that our math is complete is to deny any potential for advancement in the field. Now ill be the first to admit that changes should be met with skepticism. But one of the beauties of math is that we can work out solutions ourselves and determine if something is true. If you plug my lambda equation into the problem given, you will see it produces a balanced equation consistent with traditional math. But this technique can make virtually ANYTHING balance out. The real issue in my eyes is the appropriate application of such a technique in the real world. There are very few situations in which anything other than a number is acceptable.

On a deeper level, this tech is only useful for contradictory data... precisely what we try to eliminate in math and science. We try to normalize our data to remove such inconsistency, chalk it up to error. But in a very few select cases, duplicity may be a fundamental property of the subject and traditional logic simply cannot be applied. Perhaps it is the very reason why a theory of everything and AGI remains elusive.

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SkyCore wrote:

All of math is a construct of the mind. A very advanced construct, sure. But every bit of it was created by man.

Gotta correct you here, we don't create mathematics we discover it. We uncover truths that were already there that were previously unknown to us individually or to the wider mathematical knowledge.

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GeorgAnatoly wrote:

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SkyCore wrote:

All of math is a construct of the mind. A very advanced construct, sure. But every bit of it was created by man.

Gotta correct you here, we don't create mathematics we discover it. We uncover truths that were already there that were previously unknown to us individually or to the wider mathematical knowledge.

The relationships exist in nature which relate to many math disciplines, yes. But the act of relation is a product of invention and the mind. Semantics really.

Does it matter if i 'discovered' or 'created' the technique? In the end it comes down to the utility of the subject: does the technique allow for the solving of duplicitous data? Yes, yes it does. If we can apply it in practice that is all that matters, the distinction between 'created' and 'discovered' is moot.

Heres a decent and digestible presentation of the issue of math's existence:
https://www.youtube.com/watch?v=TbNymweHW4E