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Augustus de Morgan did. A very similar poem was also written in the 1700s by Jonathan Swift. A. de Morgan's version can be viewed as a modernization.
de Morgan:
Great fleas have little fleas upon their backs to bite 'em,
And little fleas have lesser fleas, and so ad infinitum.
And the great fleas themselves, in turn, have greater fleas to go on;
While these again have greater still, and greater still, and so on.
Swift:
So, naturalists observe, a flea
Has smaller fleas that on him prey;
And these have smaller still to bite 'em;
And so proceed ad infinitum.
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This question has no solution.We have to begin somewhere.Let us assume that "the first 5" starts from zero,.Zero is rational, so the first irrational must be above zero.How far above zero ?You choose.You construct an irrational just above zero and call that the first.Tell me what it is and I'll guarantee to construct one smaller than that but still above zero.Then someone else will find one smaller than mine.Little fleas have lesser fleas upon their backs to bite 'emAnd lesser fleas have smaller fleas, and so on ad infinitum.
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