Prove that ordinal arithmetic is associative

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SUMMARY

The discussion centers on proving the associativity of ordinal arithmetic, specifically the equation a + (b + c) = (a + b) + c. The user references the set theory book by Thomas Jech, which suggests using transfinite induction on the ordinal c. The conversation highlights the necessity of understanding transfinite induction to approach the proof effectively.

PREREQUISITES
  • Understanding of ordinal numbers and their properties
  • Familiarity with basic set theory concepts
  • Knowledge of transfinite induction techniques
  • Experience with mathematical proofs and induction methods
NEXT STEPS
  • Study the principles of transfinite induction in detail
  • Review the properties of ordinal arithmetic
  • Examine examples of proofs involving ordinal numbers
  • Explore Thomas Jech's set theory book for deeper insights
USEFUL FOR

Mathematicians, students of set theory, and anyone interested in advanced mathematical proofs related to ordinal arithmetic.

cragar
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Homework Statement


Let a, b, c be ordinals.
Prove that a+(b+c)=(a+b)+c

Homework Equations

The Attempt at a Solution




I looked at a set theory book by Jech and he says Prove by induction on c.
Should I look at the case where its true for c+1[/B]
 
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Come on. There's no single thing you could attempt here??
What is transfinite induction? What do you need to do for it?
 

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