Skip to content
We use only essential cookies to keep you signed in and remember your preferences. See our Cookie Policy.
TestStop
MocksPracticeResourcesIndiaBlogPricing
Sign in
Questions › DSE › DSE 2007 › Q46
2 marksMathematics › Real analysis › Metric spaces and normsModerateabout 3 min

DSE 2007 Question 46: Real analysis

For x,y∈ℜnx,y\in\Re^{n}x,y∈ℜn, let d(x,y)=max⁡{∣xi−yi∣∣i=1,…,n}d(x,y)=\max\{|x_{i}-y_{i}|\mid i=1,\ldots,n\}d(x,y)=max{∣xi​−yi​∣∣i=1,…,n}. Which of the following relations holds for all x,y,z∈ℜnx,y,z\in\Re^{n}x,y,z∈ℜn?

Tap an option to check your answer.

Answer and worked solution

Checking your account…

Plain-text version

For x,y∈ℜⁿ, let d(x,y)=max {|xᵢ-yᵢ | i=1,…,n}. Which of the following relations holds for all x,y,z∈ℜⁿ? (A) d(x,z)=d(x,y)+d(y,z) (B) d(x,z)>d(x,y)+d(y,z) (C) d(x,z)≥ d(x,y)+d(y,z) (D) d(x,z)≤ d(x,y)+d(y,z)

Also written as: For x,y in Re^n, let d(x,y)=max {|x_i-y_i | i=1,...,n}. Which of the following relations holds for all x,y,z in Re^n?

Real analysis has come up 38 times in 5 exams since 2005.

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.

Practise Real analysisMore on Metric spaces and norms

Similar questions from other papers

  • CUET-PG 2025 · Q67Match List-I (Types of Interval for variable x) with List-II (Mathematical Representation, given a,b ∈ ℝ with b>a): List-I: (A) Closed Interval; (B) Open Interval; (C)…
  • UGC-NET 2023 · Q62Consider the following statements: (A) The union of a finite number of closed sets is a closed set. (B) The empty set is an open set but not a closed set. (C) Every…
  • UoH 2021 · Q17Consider an economy with 2-goods. The set of all possible positive relative prices is given as: P = {(p₁, p₂) | p₁, p₂ > 0, and p₁ + p₂ = 1}. Identify the correct…
  • UoH 2020 · Q75Consider set X = {1/n | n is a natural number}. Then X is a,
  • DSE 2018 · Q48Let ℝ be the set of real numbers. A subset E of ℝ is said to be open if, for every x ∈ E, there exists r > 0 such that (x - r, x + r) is a subset of E. Then,

Question from the DSE 2007 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.