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Showing that an element of a transitive set is transitive (set theory) Watch

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    Hi, I'm struggling with showing that an element of a transitive set is transitive. I'm working with the definitions but am not getting anywhere - any tips?
    Thanks!
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    (Original post by crrrrrash)
    Hi, I'm struggling with showing that an element of a transitive set is transitive. I'm working with the definitions but am not getting anywhere - any tips?
    Thanks!
    Deleted - incorrect interpretation.
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    (Original post by ghostwalker)
    I don't see how an element can be transitive.

    A relation can, and showing transitivity would depend on how the relation is defined.

    Note: transitivity says if a~b and b~c, then a~c
    The op is talking about transitive sets. An element of a transitive set A is a subset of A, so by definition the element can be transitive.

    Just what I gathered from reading http://en.wikipedia.org/wiki/Transitive_set
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    (Original post by AWittierName)
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    Thanks for the clarification, I was clearly thinking about the wrong thing.
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    (Original post by crrrrrash)
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    Consider

    \{\ \varnothing, \{\varnothing\}, \{\varnothing, \{\varnothing\}\}, \{\varnothing, \{\varnothing, \{\varnothing\}\}\}\ \}

    and pay attention to \{\varnothing, \{\varnothing, \{\varnothing\}\}\}.
 
 
 
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