### ---- New Conversation @ Tue Feb 12 19:57:41 2002 ----

(19:57:41) **intriguingmisery:** excuse me, my name's Darcey and i need some math help

(19:58:16) **Yes ThatGuy:** ok

(19:58:36) **intriguingmisery:** are there more rational or irrational numbers in the universe?

(19:59:23) **Yes ThatGuy:** I'd tend to say irrational, but that's really just a gut feel

(19:59:32) **Yes ThatGuy:** what do you need to know this for?

(19:59:53) **intriguingmisery:** a class; but there's an infinite amount of rational numbers

(20:00:39) **Yes ThatGuy:** the problem you're dealing with is that you're toying with concepts of infinity

(20:01:02) **Yes ThatGuy:** one can easily assume that there is an infinite amount of prime numbers

(20:01:15) **Yes ThatGuy:** yet there are clearly more non-primes than primes

(20:01:53) **intriguingmisery:** but zero is rational

(20:02:17) **Yes ThatGuy:** yes, it is

(20:03:19) **intriguingmisery:** so shouldn't that tip the scales of to rational numbers?

(20:03:48) **Yes ThatGuy:** no, it won't even actually be close enough for that to matter

(20:05:06) **intriguingmisery:** but what makes it so obvious that there are more irrational numbers?

(20:07:00) **Yes ThatGuy:** there are a few basic assumptions (assumed at this level - they can be proven later) of numbers

(20:07:22) **Yes ThatGuy:** number theory in its current form asserts that 1) between any two rational numbers, there is another rational number

(20:07:39) **Yes ThatGuy:** 2) between any two rational numbers, there is an irrational number

(20:07:57) **intriguingmisery:** continue

(20:08:06) **Yes ThatGuy:** 3) between any two irrational numbers there is another irrational number

(20:08:19) **Yes ThatGuy:** and 4) between any two irrational numbers there is a rational number

(20:08:40) **Yes ThatGuy:** now, on a finite scale, this may seem like the sets are equal

(20:09:16) **intriguingmisery:** yes...

(20:09:32) **Yes ThatGuy:** however, do you agree that there are fewer integers than numbers with decimal places/fractions?

(20:09:55) **intriguingmisery:** yes

(20:10:28) **Yes ThatGuy:** and rational numbers are simply ratios of integral numbers

(20:11:14) **intriguingmisery:** i see, so there are far more numbers that just simply cannot be expressed as one of those ratios

(20:11:20) **Yes ThatGuy:** that's sort of it

(20:11:40) **Yes ThatGuy:** basically, it boils down to the fact that the set of all rational numbers is "countable"

(20:11:49) **Yes ThatGuy:** while the set of irrational numbers is not

(20:12:18) **intriguingmisery:** making it impossible to measure

(20:12:29) **Yes ThatGuy:** yes

(20:12:34) **Yes ThatGuy:** in a sense, more purely infinite

(20:13:00) **intriguingmisery:** may I quote you on all this?

(20:13:10) **Yes ThatGuy:** to whom?

(20:13:35) **intriguingmisery:** to whomever reads my paper

**yesthatguy (Oscar) reported that Darcey (intriguingmisery) signed on @ Tue Feb 12 20:13:46 2002**

(20:13:46) **intriguingmisery logged in.**

(20:14:06) **Yes ThatGuy:** I suppose you may, but you might want to find a more reputable source than a high school student

(20:14:46) **Yes ThatGuy:** depending on whom you're writing for

(20:14:57) **Darcey:** I know, but I have other conflicting sources. what you say makes sense

(20:15:37) **Yes ThatGuy:** is this for a school project?

(20:16:16) **Darcey:** you could call it that, in a sense

(20:17:01) **Yes ThatGuy:** what do you call it?

(20:17:26) **Darcey:** curiosity

(20:17:37) **Yes ThatGuy:** a curiosity paper?