Understanding Elements and Subsets in Set Theory

[flyingpig]

Homework Statement

Suppose A = {1,{1},{1,{1}}}

Then is {{{1}}} an element of A?

The Attempt at a Solution

I am thinking A has the elements are only 1, {1}, {1, {1}}

But {{{1}}} has only the element {{1}}

While A has the element {1,{1}}, you can't just take out the element 1 from {1,{1}}

So many brackets LOL

 

[Dick]

No, it's not in A. You can see the three elements of A. {{{1}}} definitely isn't one of them. Haven't we been through this sort of thing before?

 

[flyingpig]

No, it's not in A. You can see the three elements of A. {{{1}}} definitely isn't one of them. Haven't we been through this sort of thing before?

No that time was confusing subsets and elements

Like (last time) I couldn't figure out why {1} isn't a subset of some set (which I will call B) B = {{1},2,3}

 

[flyingpig]

thank you by the way! (this shouldn't even be in calculus and beyond LOL, I don't know why I posted it here)

 

[Dick]

No that time was confusing subsets and elements

Like (last time) I couldn't figure out why {1} isn't a subset of some set (which I will call B) B = {{1},2,3}

Ok, new confusion then. So what is it this time? {1,{1}} has two elements 1 and {1}. {{{1}}} has one element {{1}}. Why would you think they could be the same?