Originally Posted by

**rokman54** Hey guys,

I've been seeking quite some help from this forum.

It has been really helpful in my studies.

I was wondering what the difference between density and completeness is.

A dense subset S of R is defined $\displaystyle S \cap I not equal \phi \forall I $ which is a open interval in R.

Which basically means that you can draw any interval in R no matter how small, it will intersect with S.

There will always be an element of S in the real number interval line.

Completeness of R means that there are no gaps in the real number interval line.

Basically isn't being complete the same as being dense?