Questions: (In reverse order)
1)What is the function dα?
2)Why are you allowed to change the variable of integration?
3)Is α a function?
4)Is there a way to show integration is the reverse of differentiation?
5)What is a weight function?
6)What's the difference between L(P, f) and L(P, f, α)?
7)If f is bounded, is f always integrable?
8)If f has infinitely many discontinuities on an infinite interval is it not integrable?
9)Is Taylor's theorem an estimate of higher derivatives?
10)Does Taylor's theorem only tell you higher derivatives at a single point or an interval?
11)What does def 24 tell us?
12)What do thm's 5.9 and 5.10 tell us?
13)When is pointwise continuity useful?
14)What are running bumps?
15)How can a set be both open and closed?
16)What is the minimum number of elements needed in an interval?
17)How is lim x→as different from lim x→a
18)Can you take the limit of a distance function?
19)Does p have to be an element of E? as its a limit point
20)If f(I) is continuous and not strictly increasing, is the inverse of f still continuous?
21)What is a partial sum?
22)For the comparison test to the series have to be similar?
23)If lim an=a does the infinite series an converge?
24)How do you prove a set is compact?
25)Can a set be closed and bounded but not compact?
26)Why is S open in S?
27)Does a distance function apply to functions?
28, 29, 30)
31)If you want to prove the limit of a sequence can you use sequential limits?
32)Can you have a subsequence with one term?
33)Can you have a subsequence with infinite terms?
34)Is a constant function increasing or decreasing?
35)Does a function need to be oscillating to be Cauchy?
36)If lim tn=s and sn=s does tn=sn?
37)Is {r ∈ Q : r ≤ a} a set of r's or a's?
38)What's the difference between R ∪ {-∞, ∞} and just R?
39)What properties of R hold for {-∞, ∞}
40)Why is [a, ∞) closed?
41)Are -∞ and ∞ bounds for infinite sets?
42)Does the completeness axiom hold for complex numbers?
43)Can sup and inf be elements of S?
44)Do sup and inf work in any plane?
45)How do we know there aren't any gaps in R?
46)Does the triangle inequality hold for higher dimensions of R?
47)How does a number r satisfy the Rational Zero Theorem?
48, 49)
50)Why don't we use a base 7 number system?