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So I was thinking about slitting D into two sets C[itex]_{1}[/itex] and C[itex]_{2}[/itex] both of cardinality d. From there I think that there are d[itex]^{d}[/itex] subsets that contain C[itex]_{1}[/itex]. Since d is an infinite cardinal d[itex]^{d}[/itex]=2[itex]^{d}[/itex].

Does that work or am I missing something>