# ! Exercise 3.5.1 : On the space of nonnegative integers, which of the following functions are...

## Question:

On the space of nonnegative integers, which of the following functions are distance measures? If so, prove it; if not, prove that it fails to satisfy one or more of the axioms.

(a) max(x, y) = the larger of x and y.

(b) diff(x, y) = |x - y| (the absolute magnitude of the difference between x and y).

(c) sum(x, y) = x + y.

## Distance Measure:

Distant Measure is defined as the characteristics which are used to prove the similarity or dissimilarity between two sets of data points. The distant measure is generally calculated on the basis of Euclidian distance, Manhattan distance and Chebychev Distance.

## Answer and Explanation:

(a) max(x, y) = the larger of x and y.

The above function is not a distance measure.

Let us suppose x >0 then max(x x) {eq}= x \neq 0 {/eq}...

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