Boundness

Question 1

A number l is a least upper bound of set A if?

Answer 1

1. l is an upper bound of A.
2. If y is an upper bound of A, then l ≤ y.

Question 2

In the real numbers, every Cauchy sequence?

Answer 2

Converges.

Question 3

Is a least upper bound unique?

Answer 3

Yes

Question 4

What does it mean for a least upper bound to be unique?

Answer 4

It is a set X that belongs to itself, X.

Question 5

trichotomy?

Answer 5

A division into three possible categories in which x and y can either be x < y, x = y, x > y.

Question 6

Partial order?

Answer 6

A division into three possible categories in which x and y can me in more than one category, x < y, x = y, x > y.

Question 7

If a non-empty set A is bounded from above, then A has a?

Answer 7

Least upper bound l.

Question 8

If a non-empty set A is bounded from below, then A has a?

Answer 8

Greatest lower bound l.

Question 9

Supernum (sup A)?

Answer 9

least upper bound of set A.

Question 10

infimum (inf A)?

Answer 10

greater lower bound of set A.

Question 11

If a_n is non-decreasing and bounded above, then a_n?

Answer 11

converges.