Understanding the Power Set of a Set X: Proving Its Existence | Homework Help

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Homework Help Overview

The discussion revolves around proving the existence of the power set of a set X, specifically the set defined as {Y: Y is a subset of X}. Participants express uncertainty about where to begin and the abstract nature of the concept.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss their understanding of sets and subsets, with one expressing a desire to connect the concept to their knowledge of injective functions. Questions arise regarding the definition of a set and the implications of defining a power set.

Discussion Status

The discussion is ongoing, with participants sharing their thoughts and uncertainties. Some guidance is offered in terms of exploring definitions and the nature of sets, but no consensus or resolution has been reached.

Contextual Notes

Participants mention a lack of a formal definition for a set, relying instead on an informal understanding of sets as unordered collections of objects. This may influence their reasoning and approach to the problem.

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Homework Statement



Let X be a set. Then the set

{Y:Y is a subset of X}

prove this is a set.Where do i start?

Really unsure, i know that i have to use the power set?

I have written down;

{0,1}^X
 
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What techniques have you learned so far? And what level of math is this for?
 
undergraduate analysis.
I know how to prove basic things, like umm.
If f and g are both injective then so is g composed with f etc.
i want to say that it is a collection of unordered objects and is therefore a set. (Waste of words, i know)

It just seems WAY to abstract, the fact that {Y: Y is a subset of X} is a set of subsets of a set, surely proves that it is in fact a set! :(.
 
What formal definition of "set" are you told to use?
 
there is no formal definition, there is an informal definition that says that:

We define a set A to be any unordered collection of objects.
 

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