There [are/is] one blue button and no red button

Hi!

Among the following sentences, could you please tell me, among the following sentences, which one is correct and why? Or maybe both are OK.

  1. On this machine, there is one blue button and no red button.
  2. On this machine, there are one blue button and no red button.

Thank you very much.

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There is a blue button on this device and no red button.

There is a blue button on this device and no red button.

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?

Thank you for being so quick to answer.

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There is almost certainly exactly one infinite cluster of white objects and no infinite cluster of black objects.

When you talk about a cluster, you must specify the objects that make up the cluster.

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Thank you very much!

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.

Thanks again.

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