anonymous
  • anonymous
which group of numbers are more numerous? A. rational B. irrational
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
http://answers.yahoo.com/question/index?qid=20081129115431AAzAtYD
anonymous
  • anonymous
a theoretical question, i just want your insights!
alexwee123
  • alexwee123
i would go w/ irrational cuz they are uncountably infinte

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alexwee123
  • alexwee123
here http://everything2.com/index.pl?node_id=1259484.
anonymous
  • anonymous
irrational right?
anonymous
  • anonymous
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 \(\ \Huge \infty !\)
anonymous
  • anonymous
yeah because between 1 and 2 there can be an infinite
anonymous
  • anonymous
yeah, perhaps you're right! basing on grammar and language rule,. but i think in other sense, rational are more in number than irrational..
anonymous
  • anonymous
infinity times infinity is more than infinity
anonymous
  • anonymous
I think both are numerous. There's an infinite amount of rational numbers, and an infinite amount of irrational numbers. Both go \(\ \huge \rightarrow \infty . \)
anonymous
  • anonymous
\(\ \Huge \pm\infty that is \).
anonymous
  • anonymous
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.
anonymous
  • anonymous
Oh @nbouscal hit the spot!!
anonymous
  • anonymous
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.
anonymous
  • anonymous
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".
anonymous
  • anonymous
Why do you hate to accept it? Have you seen and understood Cantor's diagonal argument? It is quite intuitive once you understand it.
anonymous
  • anonymous
may i have the website of it?
anonymous
  • anonymous
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
anonymous
  • anonymous
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).
anonymous
  • anonymous
i'm not yet convinced. but, anyway, thanks for the ideas.
anonymous
  • anonymous
If you are not yet convinced then you simply have not yet understood the argument :)
anonymous
  • anonymous
i haven't read it yet! :-)

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