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

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

What does the phrase "partition of [tex]R[/tex] into maximal connected intervals" mean?

The full sentence: "Let [tex]I_1, I_2, ... ,I_m[/tex] be the partition of [tex]R[/tex] into maximal connected intervals with disjoint interiors."
 
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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).