Understanding Elements and Subsets in Set Theory

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Homework Help Overview

The discussion revolves around set theory, specifically examining the elements and subsets of a given set A = {1, {1}, {1, {1}}}. Participants are questioning whether {{{1}}} is an element of A and exploring the distinctions between elements and subsets.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are analyzing the elements of set A and comparing them to {{{1}}}. There is a focus on the structure of sets and the implications of nested elements. Some express confusion over the relationship between elements and subsets, referencing previous discussions on similar topics.

Discussion Status

The discussion is ongoing, with multiple participants expressing their views on the relationship between the elements of A and the proposed element {{{1}}}. Some guidance has been offered regarding the definitions of elements and subsets, but no consensus has been reached.

Contextual Notes

There is a mention of previous confusion regarding subsets and elements, indicating that participants are grappling with foundational concepts in set theory. One participant notes the inappropriate categorization of the thread under calculus, suggesting a potential misunderstanding of the subject matter.

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

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