Why is this statement true?

Question

This question is about sets:

 

{0} is not an element of {0}

 

Why is this statement true?

Answer 1

because the set {0} only contains 0. { } denotes a set, and the elements are what is inside the { }, separated by commas.

 

examples:
{0,{0}} is a set consisting of 0 and {0}
{A, B, C} consists of A, B, and C

{A, empty set, 0, {empty set}} consists of A, empty set, 0, and {empty set}

 

more complex:

{0, {0, {0}}} is a set consisting of 0 and {0,{0}} (two elements)

Note that {0,{0}} is an element of the set {0, {0, {0}}}, but by itself

{0,{0}} is a set consisting of 0 and {0}.