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jerwyn_gayo

  • 2 years ago

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

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  1. anusha.p
    • 2 years ago
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    http://answers.yahoo.com/question/index?qid=20081129115431AAzAtYD

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

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

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

  5. Romero
    • 2 years ago
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    irrational right?

  6. Study23
    • 2 years ago
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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 \(\ \Huge \infty !\)

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

  8. jerwyn_gayo
    • 2 years ago
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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..

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

  10. Study23
    • 2 years ago
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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 \(\ \huge \rightarrow \infty . \)

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

  12. nbouscal
    • 2 years ago
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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.

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

  14. nbouscal
    • 2 years ago
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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.

  15. jerwyn_gayo
    • 2 years ago
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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".

  16. nbouscal
    • 2 years ago
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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.

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

  18. nbouscal
    • 2 years ago
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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

  19. nbouscal
    • 2 years ago
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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).

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

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

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

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is replying to Can someone tell me what button the professor is hitting...

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