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    Hey everyone.

    I'm starting this area of maths and I don't understand why the relation,  \in , is a linear/total order.

    How does this relation satisfy irreflexivity and trichotomy?

    Thanks.
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    I don't think it is a total order... what set are you working on? I mean, 3 \in \{ 3 \} and \{3 \} \in \{ \{ 3 \} \} but 3 \not \in \{ \{ 3 \} \}, so it's not transitive. I'll probably find out that I've misunderstood your question.
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    (Original post by nuodai)
    I don't think it is a total order... what set are you working on? I mean, 3 \in \{ 3 \} and \{3 \} \in \{ \{ 3 \} \} but 3 \not \in \{ \{ 3 \} \}, so it's not transitive. I'll probably find out that I've misunderstood your question.
    Well it's dealing with ordinals I believe. It's a side-note in my notes; if x is an ordinal, then so is S(x).
    I'm not entirely sure what S(x) means, but I have written that  S(x) = x \cup \{x\} .

    I tried proving transitivity with: If  y \in x, x\in S(x) \Rightarrow y \in S(x)

    Thanks for the help, I'll rep afterwards.
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    (Original post by Shadow!)
    Well it's dealing with ordinals I believe. It's a side-note in my notes; if x is an ordinal, then so is S(x).
    I'm not entirely sure what S(x) means, but I have written that  S(x) = x \cup \{x\} .

    I tried proving transitivity with: If  y \in x, x\in S(x) \Rightarrow y \in S(x)
    Ah alright, this is out of my realm of knowledge I'm afraid (until early December-ish when I get round to studying ordinals, but you'll probably want an answer before then).
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    (Original post by nuodai)
    Ah alright, this is out of my realm of knowledge I'm afraid (until early December-ish when I get round to studying ordinals, but you'll probably want an answer before then).
    Ah well thanks for the intention to help anyway!
 
 
 
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