Recent content by hb123

The thing is, though, I need to show that this is true for all ε, not just an arbitrary one. On the other hand, if I'm trying to prove that the series doesn't converge to a p, then I'd need to show that !(∀ϵ>0)(∃N∈P)(∀n≥N)(| pn-p| < ϵ), or (∃ϵ>0)(∀N∈P)(∃≥N)(|pn-p| \geq ϵ). Just to clarify, P is...

Homework Statement Let {pn}n\inP be a sequence such that pn is the decimal expansion of \sqrt{2} truncated after the nth decimal place. a) When we're working in the rationals is the sequence convergent and is it a Cauchy sequence? b) When we're working in the reals is the sequence...