- #1
sg001
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Homework Statement
If s (0,1), find
|P(S)|, |P(P(S))|, |P(P(P(S)))|
Homework Equations
The Attempt at a Solution
|P(S)| = {(0), (1), (0,1), ∅} = 4
|P(P(S))| = {...} = 16.
|P (P(P(S)))| = {...} = 16 ^4 ...but how?
as my lecturer explained it, it come from pascals triangle
where the number of elements in the original set corresponds to the number from the triangle. So far so good, so in |P(S)| it contains 4 elements as shown above. Hence |P(P(S))| is equal to the sum of the corresponding (4) row of the triangle (1,4,6,4,1) = 16.
But from this logic |P(P(P(S)))| should equal the sum of the (16) expansion, but this isn't the case... can some one explain why... what it is it that I'm not getting?