Actually, my proper sentence is more technical, for a mathematical talk. I want to say “There is almost surely exactly one infinite white cluster and no infinite black cluster”.
(“almost surely” is here a technical adverb with a precise meaning in probability theory)
Is the sentence good as it is or should it be modified?
I’ll also remember what you said about the word “cluster” in English. In this particular case, “cluster” is used in a very technical sense so I believe “mathematical grammar” may prevail here over the true English meaning and use of the word.