On May 10 2009 23:15 silynxer wrote:
Damn it's hard to write about math in english, I'll try to clarify: you can't say a_n -> a if you do not have this a, so we try to define the real number a over the equivalence class of all rational sequences a_n that get infinetly close to our unknown a and thus infinetly close to each other.
Damn it's hard to write about math in english, I'll try to clarify: you can't say a_n -> a if you do not have this a, so we try to define the real number a over the equivalence class of all rational sequences a_n that get infinetly close to our unknown a and thus infinetly close to each other.
Yup, but you can still say that a_n -> 0, because 0 is a rationnal number.
So you can define two cauchy sequences (u_n) and (v_n) to be equivalent iff (u_n-v_n)->0.
(as you remark, this is just another way of saying that they will be infinitely close to each other).
(By the way, there is another fun way to construct the real, by using Dedekink's cut).