Metric Definition Quizzes, Questions & Answers

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Counterexamples and Applications of Metrics

Not every “distance” is a metric! In this quiz, you’ll explore counterexamples and real applications of metric definitions. Try this quiz to sharpen reasoning in analysis.

Questions: 15 | Attempts: 32 | Last updated: Jan 21, 2026

Sample Question 1
Which of these defines a metric on ℝ?

D(x,y)=|x−y|

D(x,y)=(x−y)²

D(x,y)=x+y

D(x,y)=√|x−y|

Sample Question 2
D(x,y)=(x−y)² satisfies all metric properties.

True

False

Sample Question 3
Which property fails for d(x,y)=|x−y|−1?

Non-negativity

Symmetry

Identity

Triangle inequality

Recent Metric Definition Quizzes

Properties of Metrics in Mathematics

Distance matters. In this quiz, you’ll practice checking the properties that define a metric. Take this quiz to build intuition for metric spaces.

Questions: 15 | Attempts: 13 | Last updated: Jan 21, 2026

Sample Question
A metric on a set X is a function d: X×X → ℝ such that:

D(x,y) ≥ 0

D(x,y)=0 iff x=y

D(x,y)=d(y,x)

Triangle inequality holds