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knowLittle
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Set Theory -- Uncountable Sets
Prove or disprove.
There is no set A such that ##2^A## is denumberable.
A set is denumerable if ##|A| = |N|##
My book shows that the statement is true.
If A is denumerable, then since ##|2^A| > |A|, 2^A ## is not denumerable.
I don't understand why they state that 2^A > A? I thought that in denumerable sets you can't really say that there is one set greater than other? I thought that there is denumerable or uncountable and that's it.
But, there is not a denumerable set greater than another denumerable set.
Help please.
Homework Statement
Prove or disprove.
There is no set A such that ##2^A## is denumberable.
The Attempt at a Solution
A set is denumerable if ##|A| = |N|##
My book shows that the statement is true.
If A is denumerable, then since ##|2^A| > |A|, 2^A ## is not denumerable.
I don't understand why they state that 2^A > A? I thought that in denumerable sets you can't really say that there is one set greater than other? I thought that there is denumerable or uncountable and that's it.
But, there is not a denumerable set greater than another denumerable set.
Help please.