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What does {{2}} mean in set theory?

{{2}} is one of the subsets in a power set of {0, {1}, {{2}}}
Not sure what it means though?
Original post by lightningdoritos
{{2}} is one of the subsets in a power set of {0, {1}, {{2}}}
Not sure what it means though?


I think the statement is false. The power set of a set S is the set that contains all subsets of S. So the power set of {A,B,C) is { {},{A},{B},{C},{A,B},{A,C},{B,C},{A,B.C}}.

2 is a number
{2} is a set with just one element - the number 2
{{2}} is a set with just one element - the set that contains just the number 2.

So {{{2}}} is an element of the power set given.

Apologies if this breaks the 'no full solution' rule.
{{2}} is:

The set containing {2}, which is:

The set containing the set containing 2
Original post by lightningdoritos
Sorry I don't think I explained it very well. The question was to write what the power set is and X={0, {1}, {{2}}}

does this mean I can't just write P(X)={ {0}, {{1}}, {{{2}}}, {0, {1}}, {0, {{2}}}, {{1}, {{2}}}, {0,{1},{{2}}}, empty set} ??


I think you've got that right :smile: Although I went cross-eyed balancing the braces!

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