Hey there! Sign in to join this conversationNew here? Join for free

Set Theory. Cartesian product of generalised union. watch

    • Study Helper
    • Thread Starter
    Online

    13
    Study Helper
    This is a question taken from "The Foundations of Mathematics" by Stewart and Tall (2nd edition).

    Name:  Untitled.jpg
Views: 21
Size:  13.0 KB

    My query is with the statement "Show that in the first formula we cannot replace '\subseteq' with '='. I can see no justification for it not being equality.

    I've checked both editions of the book, and that phrase is in each, though they have changed the notation slightly - which makes me think they have looked at the question and think that statement should stand. First formula, in the 1st edition, used to read:

    (\cup S)\times (\cup T) \subseteq \cup (S\times T)
    Edit: Corrected above line.

    Working

    Looking at that first formula, just the part to show RHS is a subset of LHS.

    Let z=(x,y) be an element of the RHS.

    Then z\in X\times Y for some X\in S,Y \in T

    And x \in X, y\in Y

    Then x\in \cup S, y\in \cup T

    So, z=(x,y)\in (\cup S)\times (\cup T) and is an element of the LHS.

    Am I missing some subtlety there, or is the book in error. Any thoughts appreciated.

    G.
    Offline

    17
    ReputationRep:
    Can't see anything wrong with your argument.
    • Study Helper
    • Thread Starter
    Online

    13
    Study Helper
    (Original post by DFranklin)
    Can't see anything wrong with your argument.
    Thanks - PRSOM.
 
 
 
Poll
Do you agree with the PM's proposal to cut tuition fees for some courses?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.