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.

{1/10, 1/20, 1/30, 1/40, 1/50, ...}

The general term of the set is _? (Type an expression using n as the variable. Use integers or fractions for any numbers in the expression)

Given the first term of the proper subset, type the next 3 terms and the general terms of n. Remember that to be considered a proper subset, the values must also be included in the original set.

{1/10. 1/20, 1/30, 1/40, ..._}

{1/30. _, _, _, ..., _}

(Type integers of fractions.)

Explanation / Answer

The general term of the set is: 1 / (10*n), where n =1,2,3,4,....

So the series becomes, 1/10, 1/(10*2) . 1/(10*3), 1/(10*4),.... i.e. 1/10, 1/20, 1/30, 1/40,....(Ans).

The next three terms of the set is 1/(10*5), 1/(10*6), 1/(10*7) i.e. 1/50, 1/60, 1/70. (Ans).

The first term of the proper subset = 1/30.

The general term of the proper subset = 1 / (30*n), n = 1,2,3,4,....(Ans).

The next three terms of the proper subset = 1/(30*2), 1/(30*3), 1/(30*4) i.e. 1/60, 1/90, 1/120. (Ans).

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