limx→01/(x2-1)=-1
0<|x|<δ and |((1/(x2-1)) +1)<ε
Working on the second equation, I eventually got
|x|< (ε|x-1||x+1|)0.5
Suppose I restrict |x|<1
-1<x<1,
then
0<x+1<2 → |x+1|<2
-2<x-1<0 → 0<1-x<2 → |1-x|=|x-1|<2 (Is this step correct? In one of the textbooks, it says that we must...
Homework Statement
Let S and T be nonempty sets of real numbers such that every real number is in S or T and if s \in S and t \in T, then s < t. Prove that there is a unique real number β such that every real number less than β is in S and every real number greater than β is in T.
The Attempt...
Hello guys! Which do you guys think is better, an honours degree (an additional year at the end of my undergrad degree usually involving a mixture of research and coursework) or a masters degree? I'll be starting my BSc (intending in Maths and Physics or Computer Science) at the Australian...
Oh I think I sort of get it. I thought 'unless' might imply something that I might have missed, because in my mind, if 'unless' could simply be replaced by 'or', then they would have written 'or' in the first place. Ah, this Maths stuff is killing me. Thanks a lot! :)
Prove that if x satisfies
'xn +an-1xn-1+ ... a0=0'
for some integers an-1,..., a0, then x is irrational unless x is an integer.
My main question is that I don't quite understand what the question is trying to ask me prove. I'm fairly new with this so pardon me if this question is really basic...