---- 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?