How can i prove a number is irrational number?

由於證明一個數字是無理數必須證明它無法寫成一個整數的分數。
想想看，你怎麼可能證明一件事是沒可能的呢？不容易吧

所以差不多所有的證明都是用反證法。具體來說，就是說，就是假設你要證明的數字是有理數而得出不可能的結論。

這些都是一些例子。

http://hk.knowledge.yahoo.com/question/?qid=7007050804287
http://hk.knowledge.yahoo.com/question/?qid=7006051302895
http://hk.knowledge.yahoo.com/question/?qid=7006090603124 [難!]

using contradiction
e.g. prove complex number 'i' is an irrational number

suppose X and Y are rational number,i is also a rational number
so X/Y=i
take square both sides
X^2/Y^2= -1
it make contradiction
square of a number could not be negative
so complex number 'i' is an irrational number

2007-09-12 16:29:03 補充：
suppose √2 is not a irrational nolet √2=p/q,the HCF between p and q is 1,p and q is integers2=p^2/q^22q^2=p^2so p is an even no

2007-09-12 16:29:17 補充：
let p=2m,m is an integer(2m)^2=p^24m^2=2q^2q^2=2m^2so q is an even no. toop and q are even no,their HCF is not equal to 1(at least 2)it make contraductionso √2 is an irrational no