... The cardinality of the set (A^B)^C is (a^b)^c. The cardinality of the set A^(BxC) is a^(bxc). But , as we already proved, the sets (A^B)^C and A^(BxC) are ...

... B and B x A have equal cardinality by constructing an explicit bijection between the two sets. Then use the following proposition to prove that multiplication ...

... 3a,What is the cardinality of the set of all finite subsets of R? Prove your answer is correct. Solution: The cardinality of set of all finite subsets of R is ...

... for 2. Thus, (B union A_(n+1)) is finite and and its cardinality is equal ... to ((A_1 union A_2 union...union A_n)union A_(n+1)). Therefore we proved the validity ...

... that every open cover of X has an irreducible subcover, and we prove that X ... Let m be the least cardinal number such that U has a subcover of cardinality m, let ...

... The first part of the problem consists of proving that $ and % have certain properties ... to the set of equivalence classes; another is that the cardinality of the ...

... x]/(f(x)) Z/(p). Obviously, Z[x] is infinite (since its cardinality is equal ... therefore M can not be a maximal ideal, contradiction.Thus we have proved that M ...

... 0 + a ⋅ 0 = 0 + 0 . We obtain a ⋅ 0 = 0 . Similarly one can prove that 0 ... implies that R and its image under the constructed map have the same cardinality . ...