Statements, sets, relations
N, Z, Q, R, C
Limits and Continuity
Derivatives and integrals
Sequences and series
100
{x | x ∈ A or x ∈ B}
What is the union of A and B?
100
i2
What is -1?
100
An example of a function f: ℂ → ℂ that is continuous everywhere.
What is f(x)=0? (Or any other valid example)
100
The derivative of x3.
What is 3x2?
100
The limit of the sequence {1⁄n}.
What is 0?
200
A function f: A → B such that for all b ∈ B there exists a ∈ A such that f(a)=b.
What is surjective?
200
The reason why ℤ is not a field.
What is lack of multiplicative inverses?
200
The limit of 1/x2 as x goes to 0.
What is infinity?
200
The integral of x3 from 0 to 1.
What is 1/4?
200
A sequence whose terms are getting close to each other as n grows.
What is a Cauchy sequence?
300
A binary operation on a set A.
What is a function A × A → A?
300
The smallest possible inductive set.
What is the set of natural numbers? (Or what is ℕ?)
300
An example of a function f: ℝ → ℝ that is not continuous anywhere.
What is the function f such that f(x)=0 if x is rational and f(x)=1 when x is irrational? (or any example of this sort)
300
A necessary condition for differentiability.
What is continuity?
300
The radius of convergence of the geometric series ∑ xk
What is 1?
400
An equivalence relation.
What is a relation that is reflexive, symmetric and transitive?
400
The set of all equivalence classes of pairs (a,b)∈ ℕ×ℕ under the relation (a,b)~(c,d) if a+d=c+b.
What is ℤ?
400
If f:[a,b]→ℝ is continuous and k is between f(a) and f(b), then there exists c∈(a,b) such that f(c)=k.
What is the intermediate value theorem?
400
The infimum of all upper sums with respect to all partitions.
What is the upper integral?
400
The value of the series ∑ (-1)k.
What is non-existent?
500
The negation of "P and (not Q)"
What is the negation of "if P then Q"?
500
The main feature that distinguishes ℝ from ℚ?
What is the existence of least upper bounds?
500
The definition of the limit of f(x) as x approaches a.
What is L such that "for all 𝜖>0 there exists ẟ>0 such that for all x in the domain of f, if 0<|x-a|<ẟ, then |f(x)-L|<𝜖?
500
An example of a bounded function f: [0,1]→ℝ that is not integrable.
What is the function f such that f(x)=0 if x is rational and f(x)=1 when x is irrational? (or any example of this sort)
500
The Taylor series for this function around 0 is ∑ xk/k!
What is ex?
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