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The largest number is about 45,000,000,000, although mathematicians suspect that there may be even larger numbers. (45,000,000,001?)
Set theorists sometimes remark that there are only very few natural numbers. I think this can be made more quantitative: Based on observations of their blackboard drawings and accompanying explanations, my current best estimate is that there are about five to ten. However, so far, my confidence in this estimate is only moderate; I still think the number could ultimately turn out to be as high as twenty.