/sci/ - Science & Math

I can follow it but am lost due to lack of knowledge.

don't subsets refer to variables inside the set?

Wouldn't a set that just contained four elements lack subsets, and if not how can there be 16 subsets? where are they?

Maybe I just don't know what the word subset really means.

The answer is there, whats the issue?

>>5688707
If he doesn't understand it then of what use is it to him in the long run?

>For a set with n elements, the number of subsets of the set is 2^n.

The only time I've really ever seen 2^n used is when referring to binary numbers. For example, if you have 4 digits, you can count from anywhere from 0 (0000) to 16 (1111). This can be expressed as 2^4 = 16.

If you take the 0s and 1s and replace them with letters, it would look something like this:
0000 =
0001 = m
0010 = a
0011 = am
0100 = o
.
.
1101 = fom
1110 = foa
1111 = foam

Just like there's 16 ways to arrange the numbers, there's 16 ways to arrange the letters. Let's call these arrangements "subsets". But what about "proper subsets"? Well, since 0000 contains no letters, it's not really arranging anything, is it? Remove that from the list, and you'll end up with the 15 proper subsets.

>>5688683
....
I think I might be retarded also, since I didn't understand this....

>>5688853
Actually, it's 1111 or {foam} that isn't a proper subset. Proper subset of a set X are strictly included in X, meaning they are a subset of X which is different from X.

The rest is correct, the proof that there are 2^n subsets to a set of n element follows is exactly what you intuitively explained here.

>>5688853
A porpet subset is a subset that isn't the whole set. The empty set is a proper subset of every non-empty set.

>>5688870
>>5688872
Alright, thanks for the heads up. I was making a guess.