Cauchy Sequence
AllPages
RecentChanges
Links to this page
Edit this page
Search
Entry portal
Advice For New Users
Think of a sequence of dots on a plane (or line). Let's suppose that they have the following property:
You give me a coin.
I can find a place to put the coin such that
all but finitely many points are covered.
This
work
s no matter how small the coin is.
In effect, we are asking that the points approach a limit. The reason for stating it as we have is because the limit point might not be in the
set
itself.
Such a sequence is called a
Cauchy Sequence
.
Here are some examples on a line:
1/2, 3/4, 7/8, 15/16, 31/32, ...
1, 3/2, 7/5, 17/12, 41/29, 99/70
Here are some sequences that are
not
Cauchy Sequence
s:
1, 2, 3, 1, 2, 3, 1, 2, ...
1, 2, 3, 4, 5, 6, 7, 8, ...
1, -1, 1, -1, 1, -1, ...
Cauchy sequence
s are a method used to construct the
real number
s from the
rational number
s.
Links to this page
/
Page history
/
Last change to this page
Recent changes
/
Edit this page
(with sufficient authority)
All pages
/
Search
/
Change password
/
Logout