Set Theory Questions (check if right)

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SUMMARY

The discussion centers on the misconceptions regarding the number of rational numbers between 4 and 6. Participants clarify that there are infinitely many rational numbers in this interval, specifically highlighting the sequence defined by $4 + \dfrac{1}{n}$ for natural numbers n. One user initially misinterprets the concept of countability in set theory, leading to confusion about the nature of rational numbers. The consensus confirms that the set of rational numbers between any two distinct real numbers is indeed infinite.

PREREQUISITES
  • Understanding of basic set theory concepts
  • Familiarity with rational and irrational numbers
  • Knowledge of countable versus uncountable sets
  • Basic mathematical notation and sequences
NEXT STEPS
  • Study the properties of rational numbers in real analysis
  • Learn about countable and uncountable sets in set theory
  • Explore sequences and their limits in calculus
  • Review examples of infinite sets and their cardinalities
USEFUL FOR

Students of mathematics, educators teaching set theory, and anyone interested in understanding the properties of rational numbers and their implications in mathematical discussions.

ertagon2
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Could someone please check if these are right?
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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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