# All Questions

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### Two definations of the dynkin system. [closed]

In this article, there are two definitions of the Dynkin system. I want to prove they are equivalent. How to use the second definition to prove the second item in the first definition?
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### Seeking proof using mathematical induction

$$a: \mathbb N ×\mathbb N \to \mathbb R$$ where for all $$x,y\in\mathbb N$$$$a(x,y) =a(y,x)$$ How do I show that the ...
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### Practice Examples of Proofs by Induction, Direct/Indirect Method

I'm learning about proofs in school, quite a few different sorts (but not geometry ones), but the teacher is teaching by slides mainly, not books. The main ones are proof by ...
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### Is this extension of ZFC known to be outright inconsistent?

Is the following first-order theory known to be outright inconsistent? Adjoin to ZFC a unary function $U$ together with the following axioms. If $\alpha$ is an ordinal, then there exists an ...