Proving Equivalence of Sets - One-to-One and Onto Function

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SUMMARY

The discussion centers on proving the equivalence of the sets {x|x>1} and {x|0 PREREQUISITES

  • Understanding of set theory concepts, specifically equivalence and cardinality.
  • Familiarity with functions, particularly one-to-one (injective) and onto (surjective) functions.
  • Basic knowledge of mathematical notation and inequalities.
  • Experience with mathematical proofs and logical reasoning.
NEXT STEPS
  • Study the definitions and properties of one-to-one and onto functions in detail.
  • Explore the concept of cardinality in set theory and its implications.
  • Learn how to construct functions to demonstrate equivalence or cardinality between sets.
  • Review examples of equivalent sets and their proofs in mathematical literature.
USEFUL FOR

Students studying mathematics, particularly those focusing on set theory, as well as educators seeking to clarify concepts of equivalence and cardinality in their teaching.

MathMajor
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Homework Statement


Hi, new to the Physics Forum and desperately need some help with a math analysis problem...

Prove that {x|x>1} and {x|0<x<1} are equivalent sets by writing a function and show that it is one-to-one and onto.


Homework Equations





The Attempt at a Solution

 
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The sets are not equivalent, rather they have the same cardinality.
 

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