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### Infinite Density Function - What is the mathematical name?

I can’t seem to find the mathematical term for the concept I call the ‘Infinite Density Function’. I can define it as:

“The amount of change in an infinite set by unit measure relative to the length of reciprocal space”

Here the value 0-1 is the unit measure that contains the infinite set of all reciprocal numbers. When the line is stretched to another value the infinite set gets less dense. Change refers to an alteration of the number density relative to this distance.

We know that the reciprocals values of all square numbers sums at infinity to the number 2. Whereas the infinite set of numbers in reciprocal space is contained within the unit measure of 0-1. therefore the 'Density ratio' is 2:1. But the 'density function' will be a change in this relationship. i.e mapped over pi.

Thanks in advance for any help.

btw: this is not anything to do with probability density, which has a similar name but is conceptually quite different.