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jerwyn_gayo Group Title

which group of numbers are more numerous? A. rational B. irrational

  • 2 years ago
  • 2 years ago

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  1. anusha.p Group Title
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    http://answers.yahoo.com/question/index?qid=20081129115431AAzAtYD

    • 2 years ago
  2. jerwyn_gayo Group Title
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    a theoretical question, i just want your insights!

    • 2 years ago
  3. alexwee123 Group Title
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    i would go w/ irrational cuz they are uncountably infinte

    • 2 years ago
  4. alexwee123 Group Title
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    here http://everything2.com/index.pl?node_id=1259484.

    • 2 years ago
  5. Romero Group Title
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    irrational right?

    • 2 years ago
  6. Study23 Group Title
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    Irrational. There are an infinite amount. For an example, consider 1.24 and 1.25 (completely random). There's 1.245 in between, amnd 1.246. Between those, there's 1.2455 and 1.2456. This goes on for \(\ \Huge \infty !\)

    • 2 years ago
  7. Romero Group Title
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    yeah because between 1 and 2 there can be an infinite

    • 2 years ago
  8. jerwyn_gayo Group Title
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    yeah, perhaps you're right! basing on grammar and language rule,. but i think in other sense, rational are more in number than irrational..

    • 2 years ago
  9. Romero Group Title
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    infinity times infinity is more than infinity

    • 2 years ago
  10. Study23 Group Title
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    I think both are numerous. There's an infinite amount of rational numbers, and an infinite amount of irrational numbers. Both go \(\ \huge \rightarrow \infty . \)

    • 2 years ago
  11. Study23 Group Title
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    \(\ \Huge \pm\infty that is \).

    • 2 years ago
  12. nbouscal Group Title
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    The answer is the irrational numbers. For some better understanding of why, you need to understand Cantor's work in the countability of infinite sets. The rationals are countably infinite; the irrationals are uncountably infinite.

    • 2 years ago
  13. Romero Group Title
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    Oh @nbouscal hit the spot!!

    • 2 years ago
  14. nbouscal Group Title
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    Brief coverage of the notion of countability: A set is countably infinite if it can be put into a bijection with the natural numbers. If it cannot, then it is uncountably infinite. Cantor's proof of the uncountability of the reals is known as his diagonal argument, and is a very fun proof. There are a lot of resources available on the web for learning about and understanding this proof.

    • 2 years ago
  15. jerwyn_gayo Group Title
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    our professor said, the answer is irrational.. but i hate to accept his, idea same as yours, by saying the difference in definition- "countable and uncountable".

    • 2 years ago
  16. nbouscal Group Title
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    Why do you hate to accept it? Have you seen and understood Cantor's diagonal argument? It is quite intuitive once you understand it.

    • 2 years ago
  17. jerwyn_gayo Group Title
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    may i have the website of it?

    • 2 years ago
  18. nbouscal Group Title
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    Here is a thread here on OS that may help you: http://openstudy.com/updates/4fc25b57e4b0964abc83b70b Here is Wikipedia on Cantor's diagonal argument: http://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument Here is Professor Francis Su of Harvey Mudd giving a lecture on Countable and Uncountable Sets: http://www.youtube.com/watch?v=mciBPGCvpBk

    • 2 years ago
  19. nbouscal Group Title
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    Uncountable is not at all synonymous to nonexistent, it is simply saying that you can't count them, for a specific definition of counting (bijection to the naturals).

    • 2 years ago
  20. jerwyn_gayo Group Title
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    i'm not yet convinced. but, anyway, thanks for the ideas.

    • 2 years ago
  21. nbouscal Group Title
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    If you are not yet convinced then you simply have not yet understood the argument :)

    • 2 years ago
  22. jerwyn_gayo Group Title
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    i haven't read it yet! :-)

    • 2 years ago
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spraguer (Moderator)
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is replying to Can someone tell me what button the professor is hitting...

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