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Math Help - Is it true that x = {x} ?

  1. #1
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    Is it true that x = {x} ?

    Is it true that 2 = {2} ? (Where {2} is the set containing just 2)

    If not why is this the case?

    Furthermore can we say that 2 E {{2}}?

    Thanks
    Last edited by kinhew93; January 14th 2014 at 07:41 AM.
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  2. #2
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    Re: Is it true that x = {x} ?

    Quote Originally Posted by kinhew93 View Post
    Is it true that 2 = {2} ? (Where {2} is the set containing just 2)
    If not why is this the case?
    Furthermore can we say that 2 E {{2}}?
    2\ne\{2\}~. ~2 is a natural number and \{2\} is a set containing the number 2.

    2\notin\{\{2\}\}

    Some axiomatic systems do define:
    \\0=\emptyset\\1=\{0\}\\2=\{0,1\}\\3=\{0,1,2\}\\ \vdots See Halmos.
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    Re: Is it true that x = {x} ?

    Hello, kinhew93!

    Are you really this confused on basic Set theory?


    Is it true that 2 = {2}? .(Where {2} is the set containing just 2) .No
    If not, why is this the case?

    We have 2.
    This is like having a banana.

    We have \{2\}.
    This is a paper bag containing a banana.

    These are not the same.




    Furthermore can we say that: . 2 \in  \{\{2\}\}\,? .No
    [
    2 is a banana.

    \{2\} is a bag containing a banana.

    \{\{2\}\} is a bag containing a bag containing a banana.

    We can say: . 2 \in \{2\}\,\text{ and }\,\{2\} \,\in\,\{\{2\}\}

    . . . and that's all.
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  4. #4
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    Re: Is it true that x = {x} ?

    Thanks - i know its simple I was just checking exactly what the notation meant, eg is it like a bag containing a banana or just a 'group' of one banana. thanks for clarifying
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    Re: Is it true that x = {x} ?

    Quote Originally Posted by kinhew93 View Post
    Thanks - i know its simple I was just checking exactly what the notation meant, eg is it like a bag containing a banana or just a 'group' of one banana. thanks for clarifying
    No, that is not the question you asked. A 'bag containing a banana' is NOT a banana but neither is "a 'group' of one banana". A "group" or "set" or "collection" of one thing is NOT that thing.
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