# Basic question: meaning of partition of R into maximal connected intervals

1. Feb 25, 2010

### seeker101

Basic question: meaning of "partition of R into maximal connected intervals"

What does the phrase "partition of $$R$$ into maximal connected intervals" mean?

The full sentence: "Let $$I_1, I_2, .... ,I_m$$ be the partition of $$R$$ into maximal connected intervals with disjoint interiors."

2. Feb 25, 2010

### slider142

Re: Basic question: meaning of "partition of R into maximal connected intervals"

Without knowing the context, it appears the author means that it is not possible to add another interval to the finite sequence that is connected and has disjoint interior. Ie., I1 = (-oo, 0], I2 = [0, oo).