example of pseudometric space

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Defines:
trivial pseudometric
Type of Math Object:
Example
Major Section:
Reference
Groups audience:

Mathematics Subject Classification

54E35 no label found

Comments

pseudometric d(f,g) triangle inequality

Example of pseudometric pasted from the pseudometric page:
Let X be a set, x0X , and let F(X) be functions XR . Then d(fg)=f(x0)âˆ’g(x0) is a pseudometric on F(X).

How do you prove the triangle inequality for this pseudometric?