What are some interesting properties of a smooth gradient that goes from dense in points to zero points per local volume?
What is an example of a completely uniform way to fill space with points in such a way? Can a function have a solution set that acts like such a gradient?
>>7966171
Get out comp 'sci'
>>7966208
What?
Yeah check out the Riemann zeta function it pretty much does exactly what you said. How you described it so efficiently is pretty amazing as well.
>>7966507
Get out CS scum.
We will answer your question if you rigorously define...
>point (bla bla bla trick question)
>density
>gradient
>smooth
>uniform
>fill
>space
>function
>solution
>set
>solution set
>>7966519
Please stop shitposting.
>>7966171
>What is an example of a completely uniform way to fill space with points in such a way?
Points, mathematically speaking, are infinitesimal small. You probably mean pixels.
Pixels are discrete but area is continuous. "Completely uniform" is therefore completely out of the question, you will need to define uniformity within a discrete countable area.
And for that you can use any probability density function that is linear across the entire range or span of these countable areas you are looking for.
>>7968125
No, I don't mean pixels, I'm asking about a mathematical object that I think should be definable. Perhaps not with the usual definition of a point?
>>7968210
You will need a definition of point that is entirely different from that of the mathematical definition. The latter has no width, no height, no area.
I think this is a case where you need to start with careful definitions.
I am a physicist. And where are the mathematicians that should have spotted this problem hours ago??
Can a solution set like this have a gradient-like structure? If it was possible to fully plot it, could it have a smoothly sparse border region?
>>7969315
Is there no mathematical term for this type of density?
Is there a reason why we couldn't arrange uncountably many points as a sparse object?
If you look the function sin(x) from above.
>>7968222
>And where are the mathematicians that should have spotted this problem hours ago??
i would have contributed but it seemed like there was no point
If you take the question as one about measure, the answer is no and it is because of the Lebesgue Density Theorem.
https://en.wikipedia.org/wiki/Lebesgue's_density_theorem
>>7970801
>i would have contributed but it seemed like there was no point
I hope you are attempting a joke but it is in the sign of the times that I cannot tell.
Have the mathematicians left this board or are they the frog posters infesting this place?
