Discrete Math creating functions that map sets

Asked Mar 10 '14 at 04:07

Active Mar 27 '17 at 16:30

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contruct a simple one-to-one function from $Z^+ → P(Z^+)$

How would I approach this type of problem? I'm guessing from utilizing $F: Z^+ → P(Z^+)$

I'm guessing need to find some way to map all positive integers to the power set of all positive integers.

Do I just define something like f(x) = the number of elements inside each subset of the Power set ? Thought I'm sure that wouldn't be 1-to-1 because multiple subsets are the same size in the power set.

asked Mar 10 '14 at 04:07

Snowyace

1

It would sure be nice if we could just let $f(n) = n$, but we need a set including an integer.... – Mar 10 '14 at 04:08
Because $P(Z^+)$ only contains sets of integers and not the integers themselves no? – Snowyace Mar 10 '14 at 04:22
If you set all $Z^+$ as n then would the function just be $2^n$ ? – Snowyace Mar 10 '14 at 04:30

Discrete Math creating functions that map sets

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