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Metric Definition Quizzes, Questions & Answers

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Counterexamples and Applications of Metrics

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: 13 | Last updated: Dec 10, 2025

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

Properties of Metrics in Mathematics

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: 12 | Last updated: Dec 10, 2025

Sample Question 1
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

Sample Question 2
The distance between any two points in a metric space is always non-negative.

True

False

Metric Definition Quizzes, Questions & Answers

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