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Originally Posted by dustin_archibald My reasoning was stated in the post which shows that the definition of the example set doesn't allow for the ideas you are describing. The example set of B={A} has elements with properties exactly the same as A. If what you are proposing was true
if
B = {A}
then
B = {{A},A}
then
{A}={{A},A}
However {A} <> {{A},A}. In other words the set of A does not contain the set of A since the set of A's properties are not exactly the same as those of A. The definition of the set of A is that it contains all elements whose properties exactly match those of A. A, however, is not a set, it is an item or entity. Thus the properties of A do not match the properties of the set of A
Something is not made up of itself. It is made of a number of other substances to create it. For example, a cookie is not made up of cookies. It is made up of the ingredients that, when combined, give it definition as a cookie. |
You are right, that a cookie is not made up of cookies. But a cookie
is made up of a cookie. It has to be. And also I discount your proof above because you talk about the set A and then you say that A is not a set. SO which is it? A set or not? Your logic is wrong because it assumes that something is not itself.