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Math Help - Set Term Comprehension

  1. #1
    Junior Member
    Joined
    Oct 2011
    Posts
    27

    Set Term Comprehension

    Hello all,

    I'm really having a hard time in understanding the term part in the following expression.

    Code:
    { a : N; s : PN; t : PN | a <ele> s ^ a <!ele> t )
    
    <=>
    
    { a : N; s : PN; t : PN | a <ele> s ^ a <!ele> t O (a,s,t) }


    What difference is it making the term part on the restriction and comprehension?

    Thanks

    ssharish
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  2. #2
    Junior Member
    Joined
    Oct 2011
    Posts
    27

    Re: Set Term Comprehension

    And also in the following expression

    Code:
    { s : PN; a : N; t : PN | a <ele> s ^ a <ele> t }
    And if i had to exhibit an element for the following set. We get {{2}, 1, {1,2}}

    Now the question is, the first element is {2} which is from s which is of type Power set of Natural numbers. But 'a' is not an element of s. As a {2} not equal to 2. Am i right?

    And also Iím not sure how the 1 got from a as well. So it seems like there two expression in the set comprehension which apples to s & t but not for a?

    Please help me understand.

    Thanks
    Harish
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