It is based on a paper by Jon Kleinberg from 2002. The paper mentions that an ideal clustering algorithm should have three properties.
1. Scale-invariance: Changing the scale of data shouldn't change the clustering algorithm's output
1. Scale-invariance: Changing the scale of data shouldn't change the clustering algorithm's output
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3. Consistency: If we move similar points closer and dissimilar points farther, the clustering shouldn't change.
The paper proves mathematically that it is impossible to have all the 3 properties.