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Questions › DSE › DSE 2014 › Q25
2 marks, −0.666666666666667Mathematics › Real analysis › Metric spaces and normsModerateabout 2 min

DSE 2014 Question 25: Real analysis

Let d((x1,x2),(y1,y2))=max⁡{∣x1−y1∣,∣x2−y2∣}d((x_1,x_2),(y_1,y_2))=\max\{|x_1-y_1|,|x_2-y_2|\}d((x1​,x2​),(y1​,y2​))=max{∣x1​−y1​∣,∣x2​−y2​∣} be the distance between two points on the plane. Then the circle centred at the origin with radius 111 is

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Let d((x₁,x₂),(y₁,y₂))=max {|x₁-y₁|,|x₂-y₂|} be the distance between two points on the plane. Then the circle centred at the origin with radius 1 is (A) a square with side length =1 (B) a square with side length =√2 (C) a square with side length =2 (D) a circle with radius =1

Also written as: Let d((x_1,x_2),(y_1,y_2))=max {|x_1-y_1|,|x_2-y_2|} be the distance between two points on the plane. Then the circle centred at the origin with radius 1 is

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What this question tests

This question is on Metric spaces and norms, part of Real analysis in Mathematics.

Distance functions and the properties that make them a metric.

TestStop has 5 past-paper questions on this subtopic.

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Question from the DSE 2014 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.