Counting Elements in a Set: {1,2,{3},{4,5},6,{{7}8}}

[wdulli]

Homework Statement

How many elements are in the set below?
{1,2,{3},{4,5},6,{{7}8}}

Homework Equations

The Attempt at a Solution

I heared that the best way is to take of the {} each time. But can somebody tell me the real rules for how to find solutions for this question. Cant seem to find it on the internet and in books. For this question i think its 8. I'm not really looking for the answer but more the explanation how i should solve this question. Thank you

1,2,3,4,5,6,7,8
1,2
3
4,5
6
78
7
8

 

[HallsofIvy]

The set {A, B, C, D, E, F} contains 6 "elements": A, B, C, D, E, and F.

The fact that, in this case, A= 1, B= 2, C= {3}, D= {4, 5}, E= 6, and R= {{7} 8} doesn't change that.

(There does appear to be a typo here. "{{7} 8}" should be "{{7}, 8}".)

 

[wdulli]

The set {A, B, C, D, E, F} contains 6 "elements": A, B, C, D, E, and F.

The fact that, in this case, A= 1, B= 2, C= {3}, D= {4, 5}, E= 6, and R= {{7} 8} doesn't change that.

(There does appear to be a typo here. "{{7} 8}" should be "{{7}, 8}".)

Yes sorry that was a typo and thanks for your answer, but can you explain me the rules (Because now I'm even more confused expecially that 7 isn't a own set in this set. (Correction element in this set)

 

[daveb]

Think of sets as boxes that contain items, perhaps fruit. In your case, you have a box that contains fruit, as well as additional boxes (which themselves might contain fruit or additional boxes, or may be empty). In counting the elements of a set, you only count the items that are part of that set, not part of a subset (i.e., not things contained in boxes that are in your first box).

 

[HallsofIvy]

What definition of "set" are you using?