I am asked to prove that these two sets are equivalent, so I know I must find a bijection between the two of them. But how would I go about doing this?
How can I exhibit a bijection between sets $A\times(B\times C)$ and $(A\times B)\times C$?
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functions
elementary-set-theory
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0Think: What would you map $(a,(b,c))$ to, where $a,b,c$ are elements of $A,B,C$ resspectively? – 2017-02-07
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0@ziggurism: The two set theory tags are meant to be disjoint. – 2017-02-07
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0@AsafKaragila I see. Thanks for the headsup. – 2017-02-07
1 Answers
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The map $f\colon A\times(B\times C)\to (A\times B)\times C$ should take $(a,(b,c))$ to $((a,b),c)$, where $a\in A,$ $b\in B$, and $c\in C$.