[lostatseajoshua]

I really don’t understand why not caring about the order would save space. Could you explain in simple terms please?

[jandrese]

If you care about the order then

1, 2, 3, 4 has to be stored differently than 4, 3, 2, 1, as well as 1, 3, 2, 4, and so on.

If you don't care about the order all of those can be stored in exactly the same way. Think of it like lossy compression, if you don't care about some of the detail you an ignore it (the order of the numbers in this case) and save some space.

[pavlov]

Consider the simplest case where your set members are just bits.

If you have three bits and you care about the order, that's a 3-bit number -- it can take 8 different values.

If you have those same bits but you don't care about the order, the operation is a "bit count" -- you can only have 4 different values.