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Comments:
>>>>Good answer in this context.  How could we say more generally when something like a group or ring or field should count as just a copy of something else?

>>
>>How about starting by saying that two sets which are "copies" of each other should have the same cardinality ? Matt argued that
>>we can't consider Z_7 a copy of the rationals because no 1-1 map
>>exists between Q and Z_7; that's because Z_7 isn't "big enough."
>>Similarly, the rationals probably should not be considered
>>a "copy" of the reals, since the reals are uncountable and Q
>>is countable -- so again no 1-1 map exists.

>>I don't know if every set of the same size should be considered a "copy" of every other set of the same size, but it seems like
>>someplace to start. 


 

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