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Nilanjan Bhowmick AIR 3, CSIR NET (Earth Science)
Deepikachaudhary posted an Question
March 26, 2020 • 17:18 pm
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30 points
30 points
- CSIR NET
- Mathematical Sciences
Mathematic sciences (real a 4. cantor's theorem for any set which is non-empty; to its power set onto map cannot be defined. proof let a be any set suppose 3f a
Mathematic Sciences (Real A 4. CANTOR'S THEOREM For any set which is non-empty; to its power set onto map cannot be defined. Proof Let A be any set Suppose 3f A- P(A) which is onto. Let r e A f() E P(A) f() SA (From above observation) re f) or re f(r) Define X = {re A;re f)} cA X e P(A) Since f is onto a e A such that f(a) = X or a f(a) = X a E f(a) X or a X a EX or o E f(o) which i a contradiction our supposition IS wrong Hence proved By cantors theorem, we can say Nand P(N) cannot be equivalent So we adopt new symbol to denote the cardinality of P() C PC 2= e
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Sumati priya![best-answer]()
kindly tell on which point u r facing problem.