Properties of Metrics in Mathematics

  • 11th Grade
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| Attempts: 12 | Questions: 15 | Updated: Dec 10, 2025
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1) For a metric d, d(x,x)=0 always holds.

Explanation

Identity property.

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About This Quiz
Properties Of Metrics In Mathematics - Quiz

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

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2) Symmetry means d(x,y)=d(y,x).

Explanation

Symmetry property.

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3) In the discrete metric, d(x,y)=?

Explanation

Discrete metric definition.

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4) Triangle inequality states d(x,z) ≤ d(x,y)+d(y,z).

Explanation

Triangle inequality.

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5) The distance between any two points in a metric space is always non-negative.

Explanation

Non-negativity property.

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6) Which property is violated by d(x,y)=x−y on ℝ?

Explanation

d(1,2)=−1

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7) Which property distinguishes metrics from pseudometrics?

Explanation

Pseudometric may assign 0 to distinct points.

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8) A metric on a set X is a function d: XmX → ℝ such that:

Explanation

These are the four metric axioms.

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9) Which of the following is NOT a property of a metric?

Explanation

Linearity is not required.

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10) In ℝ with d(x,y)=|x−y|, what is d(3,7)?

Explanation

|3-7|=4.

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11) Which of these is a metric on ℝ²?

Explanation

Euclidean, Manhattan, and Max norms are metrics.

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12) Which function is NOT a metric?

Explanation

x+y does not satisfy metric axioms.

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13) Which of the following is a metric on ℝ²?

Explanation

Manhattan and Euclidean are metrics.

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14) Which metric is called the Euclidean metric?

Explanation

Euclidean metric in ℝ.

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15) In a metric space, distance can be infinite.

Explanation

Distance must be finite.

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For a metric d, d(x,x)=0 always holds.
Symmetry means d(x,y)=d(y,x).
In the discrete metric, d(x,y)=?
Triangle inequality states d(x,z) ≤ d(x,y)+d(y,z).
The distance between any two points in a metric space is always...
Which property is violated by d(x,y)=x−y on ℝ?
Which property distinguishes metrics from pseudometrics?
A metric on a set X is a function d: XmX → ℝ such that:
Which of the following is NOT a property of a metric?
In ℝ with d(x,y)=|x−y|, what is d(3,7)?
Which of these is a metric on ℝ²?
Which function is NOT a metric?
Which of the following is a metric on ℝ²?
Which metric is called the Euclidean metric?
In a metric space, distance can be infinite.
Alert!