Show that the set is infinite by placing it in a one-to-one correspondence with

Question

Show that the set is infinite by placing it in a one-to-one correspondence with a proper subset of itself. Give the general term of the original set, and show its pairing with its proper subset.

{6, 36, 216, 1296, 7776, ...}

The general term of the set is _? (Type an expression using n as the variable)

Given the first term of the proper subset, type the general term. Remember that to be considered a proper subset, the values must be included in the original set.

{6, 36, 216, 1296, ..._}

{216, 1296, 7776, 46656, ...._} (Type an expression using n as the variable)

Explanation / Answer

It is a proper subset that would have a one-to-one correspondence with itself is the subset of all powers of 6 (using positive exponents).
The one-to-one correspondence is given by the formula f(n) = 6n, where n = 1,2,3,4,5,...

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