Thread: Corollary on Irrational Number

,.hello everyone,.,i need ur help agen with this,.,


Let epsilon>0 be an irrational number and let z>0. then there exists a natural number m such that the irrational number epsilon/m satisfies 0<(epsilon/m)<z.


,.i somehow understand the proof on the book but i was having a hard time proving that

epsilon/m is an irrational number,.,can anyone give me a hand with this???any hint will do,.,.thnx a lot[IMG]file:///C:/Users/User/AppData/Local/Temp/msohtmlclip1/01/clip_image010.gif[/IMG]

Your image did not load. However, given any irrational number, , there exist a real number, r, greater than , , for example. Given that, let z= r/m where m is any natural number. Then and so .