Consider the statements for : (i) ; (ii) . In general,
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DSE 2010 Question 33: Real analysis
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Consider the statements for x,y∈ℜ: (i) |x|-|y|≤ |x-y|; (ii) | x|-|y | =|x-y|. In general, (A) (i) is true and (ii) is false (B) (i) is false and (ii) is true (C) Both (i) and (ii) are true (D) Both (i) and (ii) are false
Also written as: Consider the statements for x,y in Re: (i) |x|-|y|<= |x-y|; (ii) | x|-|y | =|x-y|. In general,
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.
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Question from the DSE 2010 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.