Set Theory Questions (check if right)

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Discussion Overview

The discussion revolves around questions related to set theory, specifically focusing on the correctness of certain claims about rational numbers within a specified interval. The scope includes conceptual clarification and mathematical reasoning.

Discussion Character

  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants indicate that one part of question 1 is incorrect, while others believe everything else is correct.
  • There is a contention regarding the number of rational numbers between 4 and 6, with some participants suggesting there are only finitely many.
  • One participant questions the assertion of finitely many rational numbers by introducing the sequence $4 + \dfrac1n$ for natural numbers n.
  • A later reply reflects a reconsideration of the concepts of countable and uncountable sets.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correctness of the claims regarding the number of rational numbers between 4 and 6, indicating multiple competing views remain.

Contextual Notes

There are unresolved assumptions regarding the definitions of finite and countable sets, as well as the implications of the sequence mentioned.

ertagon2
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Could someone please check if these are right?
View attachment 7908
 

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Re: Set Theory Questions (check if irght)

ertagon2 said:
Could someone please check if these are right?
One part of q.1 is wrong. Everything else looks correct.
 
Re: Set Theory Questions (check if irght)

Opalg said:
One part of q.1 is wrong. Everything else looks correct.

Which one? Looks alright to me.
 
Re: Set Theory Questions (check if irght)

ertagon2 said:
Which one? Looks alright to me.
Only finitely many rational numbers between 4 and 6 ? (Doh)
 
Re: Set Theory Questions (check if irght)

Opalg said:
Only finitely many rational numbers between 4 and 6 ? (Doh)
Isn't there a finite number of rational numbers for 4<x<6 ?
 
Re: Set Theory Questions (check if irght)

ertagon2 said:
Isn't there a finite number of rational numbers for 4<x<6 ?
What about the numbers $4 + \dfrac1n$, for $n=1,\,2,\,3,\,\ldots$ ?
 
Re: Set Theory Questions (check if irght)

Opalg said:
What about the numbers $4 + \dfrac1n$, for $n=1,\,2,\,3,\,\ldots$ ?
Oh nvm
I was thinking about countable and uncaountable.
 

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