# How can B be an element of C?

1. Oct 26, 2013

### Venomily

Question 2 (a)

how is it possible? B is a set (since A is a set), how can a set be an element of another set?

Rather than saying: B is an element of C

I thought it would be better to say: B is a subset of C.

Also, can someone explain question 2 (d) to me? thanks

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2. Oct 26, 2013

### Venomily

im quite desperate.

3. Oct 26, 2013

### UltrafastPED

Yes, a set can be an element of another set. There may be a set X={a,b,c}, where X is an element of Y.
But neither a, nor b, nor c becomes a member of Y; only the sets are members.

But you can have a set Z = {a, X} ... so X contains a,b,c, but neither b nor c is a member of Z.

Sets are "packages", and the set Z has the package X as an element - like having an apple and a package of sausages in your shopping bag. You can reach in and pull out the apple, but you cannot pull out a sausage - only a package of sausages.

But you could reach into that package of sausages and pull out a sausage!

4. Oct 26, 2013

### UltrafastPED

2(d) is the null set. Try it with the package concept!

5. Oct 26, 2013

### Venomily

Great explanation, I understand now, thanks.

But how would I go about 2 (d)? we have the empty set, {}:

{A} = { { 0, {}, {{}} } }

Judging by what you said, I don't see how {} can be related to the above set? it is neither an element nor a set.

6. Oct 26, 2013

### Venomily

{} = sausages
{{}} = packet of sausages
0 = Orange

{ 0, {}, {{}} } = Shopping bag of (Orange + sausages + Packet of sausages).

{ { 0, {}, {{}} } } = car boot of Shopping bag.

We want {{}} i.e. the packet of sausages. It is not related to the Car boot because it is neither a SET nor a MEMBER of the Car boot, it is too deep inside.

Last edited: Oct 26, 2013
7. Nov 2, 2013

### HallsofIvy

Staff Emeritus
By the way, this is true in "Naive set theory" which suffers from "Russel's Paradox". In "class theory" we do NOT allow "sets" to be contained in sets, but have a hierarchy of "classes" in which classes in one tier can be contained in classes of a higher tier. "Sets" are the lowest tier of classes.