Suppose we decide to let 'Steve' name the successor of the largest number anyone

Suppose we decide to let 'Steve' name the successor of the largest number anyone

Suppose we decide to let 'Steve' name the successor of the largest number anyone has ever thought about before next Tuesday. Can I now think about Steve? For example can I think (or even know) that Steve is greater than 2? If not, why not? If so, wouldn't that mean that some numbers are greater than themselves?

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