The Rationals and the Reals Flashcards
1
Q
When is a set ordered?
A
- trichotomy law holds
2. transitivity holds
2
Q
What is an upper bound?
A
u is an upper bound if for all a in A, a <= u (every value in A is smaller than an upper bound)
3
Q
When is a set bounded above?
A
When an upper bound exists.
4
Q
When is a set bounded?
A
When its bounded both above and below.
5
Q
What is a maximum?
A
M is a maximum if M is an upper bound that is in the set (may not always exist)
6
Q
What is a supremum?
A
The least upper bound of a set is the supremum
7
Q
If A has a maximum …
A
max A = sup A
8
Q
What is the triangle inequality?
A
|x+y| <= |x| + |y|
9
Q
What is the reverse triangle inequality?
A
||x| - |y||<= |x - y|
