Ready Set Go Calc Review Math Words Flawless Laws Relationships

### Yang/Yayi

What is a finite set?

(A countable set is finite or denumerable.)
A set whose cardinality equals a nonnegative integer.

### Joe Fink

What is a differentiable function?
A function with non-vertical tangent lines at all points of its domain.

### Peng Zhang

What are the elements (or members) of a set?
The objects that make up a set.

### Wenxian Liang

A compound statement that is always false.

### Peng Zhang

What is the inverse of a relation?
For a relation from A to B, this is the relation from B to A.

### Yayi Wang

What is a proper subset?
Given a set S, a set A such that all elements of A are in S but not all elements of S are in A.

### Lingwen Li

What is a partial sum (of a sequence)?

(More precisely: What is the nth partial sum?)
The summation of the first n terms of a sequence.

### Ana Vieyra

What is a theorem?
A fundamental mathematical result.

### Shiyao Cao

What is a trivial proof?
The verification of a true statement from an unnecessary condition.

### Liyu Zhou

What is a function's range?
The set of images of all elements in a function's domain.

### Brett Bullis

What is the difference between two sets A and B (A-B)?
The relative complement of a set B in a set A (A ∩ B).

### Mieraf/Xin

What is a convergent series?

(A divergent series is a series whose sequence of partial sums does not converge.)
An infinite summation whose sequence of partial sums approaches a limiting value.

### Brett Bullis

What is a definition?
An initial characterization to give meaning to a (mathematical) term or concept.

### Wenxian/Xinxiayou

What is a commutative law?

(An associative law is a rule that the outcome of multiple operations between multiple
objects is independent of the order in which the operations are executed.)
A rule that the outcome of an operation between two objects is independent of their order.

### Qianmei Xing

What is an injective (one-to-one) function?
x ≠ y ⇒ f(x) ≠ f(y)

### Liyu/Mieraf

What is an ordered pair?

(The Cartesian product of n sets is the set of all ordered n-tuples.)
An element in the Cartesian product of two sets.

### Shiyao Cao

What is a Fibonnaci number?

(The sequence is 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...)
A number from the sequence that starts with two ones and continues by always adding the two preceeding numbers (also has something to do with rabbit relationships ...).

### Lingwen Li

What is an index set?
A set of subscripts used to denote different elements in a set.

### Ana/Jocelyn

What is a vacuous proof?

(Any statement about an element of the empty set is vacuously true.)
The verification of an implication by showing that its condition is always false.

### Wenxian Liang

What is a residue class (modulo n)?
An element of the integers modulo n.

### Yang Lei

What is an indexed collection of sets?
A set of sets that are denoted using a set of subscripts.

### Mieraf Shiferaw

What is the arithmetic mean (of two numbers)?
Given two numbers, the unique number whose distances to both numbers are identical.

### Xinxiayou Xin

What is an axiom?
A fundamental assumption that is neither proven nor disproven but accepted to be true.

### Jocelyn Bice

What is a proof of numerical equivalence (to show that two sets have the same cardinality)?
Establish a one-to-one-correspondance between two sets.

### Xin Wang

What is a relation?
A subset of the Cartesian product of two sets.

# Math 3000 Abstract Math Jeopardy Spring 2012 Student Edition

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