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Prove that the following set has the same cardinality (it's enough to prove it is bijective): - Any two open intervals (p,q) and (s,t) where p

Prove that the following set has the same cardinality (it's enough to prove it is bijective): - Any two open intervals (p,q) and (s,t) where p

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 13E: 13. Consider the set of all nonempty subsets of . Determine whether the given relation on is...
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Prove that the following set has the same cardinality (it's enough to prove it is bijective):

- Any two open intervals (p,q) and (s,t) where p<q and s<t and p,q,s,t are all real numbers

 (hint: let f:(p,q) → (s,t))

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I understand the process of proving 1-1 and onto, however, how did you obtain the function f(x) = ((t-s)/(q-p))(x-p)+s from f:(p,q)->(s,t)?

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