Prove that ordinal arithmetic is associative

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The discussion centers on proving the associativity of ordinal addition, specifically the equation a+(b+c)=(a+b)+c for ordinals a, b, and c. Participants suggest using induction on c as a method for the proof, referencing a set theory book by Jech. There is confusion regarding the specifics of transfinite induction and its application in this context. Questions arise about whether to consider the case where c is c+1 and how to approach the proof effectively. Clarification on transfinite induction and its steps is sought to facilitate the proof process.
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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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