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Topic: Possible error in Grzegorczyk's seminal paper on Grzegorczyk hierarchy?
Replies: 0

 Paul Posts: 780 Registered: 7/12/10
Possible error in Grzegorczyk's seminal paper on Grzegorczyk hierarchy?
Posted: Jan 8, 2014 8:05 PM

I got stuck very early on when trying to read Some classes of recursive functions, available here: http://matwbn.icm.edu.pl/ksiazki/rm/rm04/rm0401.pdf

On page 4, surely K and L are intended to be functions from the naturals to the naturals.

But, let z = 1001. Then the integral part of sqrt(z) = 31. Square that integral part and we get 961. Hence K(z) = 1001 - 961 = 40. Hence L(z) = 31 - 40 = -9. But L(z) should be positive so that we get the promised correspondence between N and N x N.

Is there a typo here, or am I missing something?

Many thanks for your help.

Paul Epstein