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You are either too clever or too clever.
The density of the cluster (clump) in a numerical series. The number series itself is not interesting - it only acts as a definition of the limits.
You have told that in the end we need the densest cluster, we have got it.
There is no certainty, as yet, that what we have got is the correct definition of the cluster....
You understand that you have found exactly a cluster of ALL series of numbers.
Precisely, I understand that you have found it and I've been telling you about it for a long time, but whether this information will be useful, is not clear yet.
Regarding "how close the numbers are to each other" - you need to automate the process of sifting out numbers that are not close - you need a criterion - logic. In my algorithm I sift out numbers by delta until they are less than half of the original series, but it can also be not enough - namely, the task - find the best criteria - one of the most difficult in this algorithm.
First of all, understand the importance and relativity. What are we trying to find?
You can't be so categorical - it hurts progress...
If you take a basin of water and throw in cubes...
It's clear - and I already wrote above, why it would be so... But, we need to consider the relation of each cube to the neighboring one...
What can we do.
We can find it, but if we know what we're looking for... which makes it difficult to find it - the reason I gave above.
About the example - theoretically, let's take the numbers and:
1. Let us increase the number series by the same number series, previously multiplying it by 1000
2. the same point as 1, but replace 56 with 59
Now the question is different.
I just add a minimum value of 1 point in my algorithm.
Adense set is a subset of space, the points of which can approximate any point of the enclosing space as good as you want.
I think I've already written about academic knowledge... Let's think within the limits of the task at hand, not theoretical inferences.
Clearly the number set is either one continuous integer or consists of regions, which are supposed to be ranked according to attributes, one of the attributes being density.