Math Quiz

[Ether]

If anybody's still interested here's the solution:

The number of proper subsets of a set containing N elements is 2^N -1.

For N=30000, the number of proper subsets is 2³⁰⁰⁰⁰ -1.

The "-1" totally insignificant for such a large N.

Find "x" such that 10^x = 2³⁰⁰⁰⁰...

take log₁₀ of both sides:

log₁₀(10^x) = log₁₀(2³⁰⁰⁰⁰) ..∴.. x = 30000*log₁₀(2) = 9030.9

10^9030.9 = 10^0.9 * 10⁹⁰³⁰ = 7.94E9030

[Nate Laverdure]

-1 is because the complete set (with all N elements) is not counted? A set cannot be a proper subset of itself?

The empty set is still counted, correct?

[Ether]

Originally Posted by Nate Laverdure

-1 is because the complete set (with all N elements) is not counted?

Correct.

A set cannot be a proper subset of itself?

Correct.

The empty set is still counted, correct?

Correct.