The midterm examination will be held Thursday, November 10th.
The exam will consist of three sections:
Obviously due to time limitations the latter set of proofs will have to be relatively short ones.
The terms will be taken from the following list:
Term | Text Reference |
one-to-one | Definition 1.29 |
onto | |
bijection | |
bounded above | Definition 1.10 |
supremum | |
bounded below | Definition 1.19 |
infimum | |
bounded | |
R,N,Z,Q | Section 1.2 p.7 |
image of a set under f | Definition 1.33 |
inverse image of a set under f | |
finite set | Definition 1.38 |
countable set | |
at most countable set | |
uncountable set | |
convergent sequence | Definition 2.1 |
subsequence | Definition 2.5 |
bounded (above/below) sequence | Definition 2.7 |
divergent sequence | Definition 2.14 |
increasing sequence | Definition 2.18 |
decreasing sequence | |
monotone sequence | |
Cauchy sequence | Definition 2.27 |
limsup | Definition 2.32 |
liminf | |
function limit (2-sided) | Definition 3.1 |
left hand function limit | Definition 3.12 |
right hand function limit | |
function limits involving infinity | Definition 3.15 |
continuity | Definition 3.19 |
uniform continuity | Definition 3.35 |
The theorems (on the matching section) will be taken from the following list:
Term | Text Reference |
fundamental theorem of absolute values | Theorem 1.6 |
approximation property for suprema | Theorem 1.14 |
completeness axiom | Postulate 3 p.18 |
Archimedean principle | Theorem 1.16 |
reflection principle | Theorem 1.20 |
monotone property | Theorem 1.21 |
well-ordering principle | Theorem 1.22 |
DeMorgan's laws | Theorem 1.36 |
at most countable characterization | Lemma 1.40 |
Bolzano-Weierstrass theorem | Theorem 2.26 |
comparison theorem (functions) | Definition 3.10 |
sequential characterization of continuity | Theorem 3.21 |
preservation of Cauchy sequences | Lemma 3.38 |