show that on the set of real numbers R the function d is defined by d(x,y) = |x - y | defines a metric?
Igor Goliney
This is done in easy steps
1. Find the definition of metric in your textbook. Wikipedia would do as well..
2. Prove a lemma |a +b|
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Biswajoy Brahmachari
d(x,x)=0 d(x,y)+d(y,z) >= d(x,z) [post of Igor] d(x,y)=d(y,x) For x not equal to y we get d(x,y) > 0
That's about all; ref: https://proofwiki.org/wiki/Real_Number_Line_is_Metric_Space
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