Number of Fantabulous integers
Level
pending
A Fantabulous number is a positive integer which has another Fantabulous number smaller than it.Find the number of Fantabulous numbers.
The answer is 0.
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Let F be the set of fantabulous integers.Assume F is non-empty.By the well-ordering principle,there exists a smallest integer f in the set.But by definition,there exists a smaller fantabulous integer in the same set,contradicting our claim that f is the smallest fantabulous integer.Thus no fantabulous integer exists.