***How many proper subsets are there of a set containing 30,000 elements?

**

*

*

(2^n)-n

(2^30,000)-30,000

(7.951x10^9030)-30000

7.851x10^9026

Almost, but not quite right.

(7.951x10^9030)-30000

7.851x10^9026

If you subtract a mere 30000 from 10^9030 you don’t get 10^9026

*If anybody’s still interested here’s the solution:

The number of proper subsets of a set containing N elements is 2N -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 10x = 230000…

take log[sub]10[/sub] of both sides**:**

log[sub]10/sub = log[sub]10/sub …**∴**… x = 30000*log[sub]10/sub = 9030.9

109030.9 = 100.9 * 109030 = 7.94E9030

-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?

Correct.

A set cannot be a proper subset of itself?

Correct.

The empty set is still counted, correct?

Correct.