Quote (chone @ May 20 2010 06:28pm)
It is NOT a real number. When I say "not a real number", this means 0.000...1 does not belong to the set of real numbers.
The set of real numbers has a property called the least upper-bound property. This property can be used to prove that the set of positive infinitesimals is EMPTY - which means THERE AREN'T ANY. (note that this proof is trivial and easy to find; hell it's probably on wikipedia)
Now, since positive infinitesimals do not exist, we cannot have a number such as 0.000...1 (because 0.000...1 implies an infinitesimal). Q E motherFUCKING D.
But wait. I'll call you out. You said it's a rational number. Then by the definition of rational numbers, 0.000...1 would be able to be written as p/q, for some integers p and q (and q is nonzero). So what are these integers? I'll help you: they don't exist. Because this number isn't rational (nor is it real).
I won't call you retarded. I'll call you fucking stupid and uneducated. Yes I'm a nerd, and I sure as fuck know a fuckton more math than you do.
Love the latin proof rage. You should teach.