Thread 16754083

I don't really know much about math but like, if you take the entire set of natural numbers and graph it as a vector it'd be like a line of indeterminate distance right. And if you do the same thing with the set of integers it would be like a bidirectional vector of indeterminate distance.

Couldn't you just re-graph that as a plane, and just include a single abstract unit length for the Y axis that represents either positive or negative of indeterminate value to represent the set of integers without having to use bidirectional vectors? Like, for any number that's positive it stays at 0, and for any number that's negative it goes to 1.

Which leads to the intuitive question, is it possible to have number sets that are "gradients" of positivity and negativity, instead of just black and white, positive or negative? How would that work?

Am I making any sense?

>>16754083 (OP)
If you take the entirety of the natural numbers and graph them, assuming the ordered pair (n,f(n)) is an element of NxN (I am too lazy for LaTeX atm), you would just have an monotonic sequence of discrete points, not a vector.

>>16754083 (OP)
look into complex numbers

>>1675408
Rather than already trying to use math terms you don't really understand (nothing wrong with that), you should try to describe in a more conceptual sense what your goal is, what you're trying to show, and what the steps would be.

>>16754083 (OP)
>take the entire set of natural numbers and graph it as a vector
If we take all of n in N as a vector, we get an n-vector of infinite size where the unit of every dimension n is n. As in, x_1 = 1, x_2 = 2, ... x_n = n, x_n+1 = n+1
>is it possible to have number sets that are "gradients" of positivity and negativity, instead of just black and white, positive or negative?
As per >>16754820, complex numbers give you picrel

>>16754820
>>16754872
Oh wow, thanks, yeah complex numbers are exactly what I was looking for! I never got that far in math. I'm trying to figure things out for myself as much as I can but sometimes I can't see the big picture...

>>16754083 (OP)
Let the cat in. He wants to help you, not hurt you.

>>16754863
I guess I'm not sure how to explain it correctly, but the intuition I had was the idea that there could be "psuedo" positive, and "psuedo" negative values, where the positive or negative property of a natural number that means it an integer could be indeterminate rather than black and white, true or false, positive or negative. Couldn't there be other states? Such as in four value logic used in IEEE stuff, where you have true, false, "don't know", and "don't care".

Like, could there be some set of numbers where the positive and negative can be more than just positive and negative. Is it possible to organize numbers in such a way that isnt reducible to addition and subtraction? Is that the basis of ALL operations? Everything just reduces back to addition and subtraction in SOME abstract way, no matter how complex the equation is, no matter how complex the formula is, no matter what mind of math it is, no matter what kind of operation it is, at the end of it all, at the end of the day, we're just adding and subtracting. Everything is just addition and subtraction, somehow, in some elaborate convoluted form, no matter what it is you're doing, no matter how complex it is.

>>16754982
Yeah, it's either addition and subtraction or pretending you can say something addition and subtraction, like the fake solution to Fermat's last theorem, by boiling an egg.

>>16754982
Here is an answer that is obviously human-powered, not just soulless AI. It essentially said what I was going to write.
I can just add that your question is essentially territory where you only get to if you studied abstract algebra and also did a lot of your own thinking.