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Describe The Vastness Of The Sets Of Rational And Irrational Numbers.

A mathematician once described the set of rational numbers as the stars and the set of irrational numbers as the black in the night sky.?

The meaning of a metaphor depends upon the context, and the reason for employing it. What was the subject of the conversation; to whom was he speaking, and what point was the metaphor intended to illustrate ? We don't know the answers to any of these, so trying to interpret the quotation is pure speculation. Half-a-dozen people could give you half-a-dozen interpretations. All of them could be right, or none of them. The only one who KNOWS what he meant is the mathematician who made the remark.

Describe the vastness of the sets of rational and irrational numbers.?

It might be asking how large both of the sets are. Both rational and irrational numbers are infinitely large, but rational numbers are countable while irrational numbers are uncountable.

The union of the set of rational numbers and the set of irrational numbers is the set of real numbers.