2 - Well-Defined Definitions

Question 1

The _____** **_____\_ of x₀ and x₁ denoted <x>0, x₁&gt; is {{x₀}, {x₀,x₁}}</x>

Answer 1

The ordered** **pair of x₀ and x₁ denoted <x>0, x₁&gt; is {{x₀}, {x₀,x₁}}</x>

Question 2

A relation in set theory is a set of ________ __-____\_.

Answer 2

A relation in set theory is a set of ordered n-tuples.

Question 3

If x is e-minimal in y, then it satisfies ____-_________.

Answer 3

If x is e-minimal in y, then it satisfies well-foundedness.

Question 4

A _____\_ is a set of ordered pairs.

Answer 4

A relation is a set of ordered pairs.

Question 5

All sets are _______, but not all ________ are sets.

When a _____** is not a set, we call this a **_____** **____\_.

Answer 5

All sets are classes, but not all classes are sets.

When a class is not a set, we call this a proper class.

Question 6

The ________** **_______\_ is the unique set C consisting of the the ordered pairs , where a is in some set A and b is in some set B.

Answer 6

The Cartesian Product is the unique set C consisting of the the ordered pairs , where a is in some set A and b is in some set B.

Question 7

A set is _____**-**_____\_ if you can prove existence and uniqueness.

Answer 7

A set is well-defined if you can prove existence and uniqueness​.

Question 8

We say that a set x is ______\_ if it contains the empty set and is closed under S.

Answer 8

We say that a set x is inductive if it contains the empty set and is closed under S.