Welcome guest
You're not logged in.
371 users online, thereof 0 logged in

The theorem of Bolzano-Weierstrass motivates the following definition:

## Definition: Accumulation Point (Real Numbers)

A real number $$a$$ is called an accumulation point of a real sequence $$(a_n)_{n\in\mathbb N}$$, if it contains a subsequence $$(a_{n_k})_{k\in\mathbb N}$$ that is convergent to $$a$$.

### Notes

• Informally, $a$ is an accumulation point $B,$ if there are points of $B$ which are arbitrarily close to $a.$
• This is a special case of a general topological definition of accumulation points.

| | | | | created: 2014-02-20 23:23:56 | modified: 2020-07-09 05:27:36 | by: bookofproofs | references: [581], [6823]