Given that sequences a and b converges respectively, to the limits L1 and L2. Use def of limit of sequence to prove that if a>=b for all natural numbers n, then L1>=L2.
Answer given is,
Suppose on the contrary that L1 < L2. Let epsilon = (L2-L1)/2
, which is positive.
Let n = max(N1;N2) + 1. Then n > N1 and n > N2. So we have
a) why are they using epsilon = (L2-L1)/2
b) what does it mean by 'n=max(N1,N2) + 1?' why using this?
calculus is really giving me headache now.