Analysis

Question 1

What is the Archimedian property?

Answer 1

Let xϵR, then ∃nϵN st n>x

Question 2

When is cϵR an accumulation point of a sequence?

Answer 2

Iff there exists a subsequence (ak)kϵN st ank–>c

Question 3

What is the ratio test for a sequence with an=/=0 for all n?

Answer 3

limsup|an+1/an| <1 converges absolutely, >1 diverges.

Question 4

What is the monotone convergence theorem?

Answer 4

Let an be bounded above and non decreasing. Then an–>sup(an).
Let an be bounded below and non increasing. Then an–>inf(an)