0AppA071110

# 0AppA071110 - 1 APPENDIX A PRINCIPAL CLASSES OF FUNCTIONS...

This preview shows pages 1–2. Sign up to view the full content.

1 APPENDIX A PRINCIPAL CLASSES OF FUNCTIONS AND SETS N is the set of all nonnegative integers. |x| is max(x). MF is the set of all functions whose domain is a subset of some N k and whose range is a subset of N. SD is the set of all f MF such that for all x dom(f), f(x) > |x|. EVSD is the set of all f MF such that for all but finitely many x dom(f), f(x) > |x|. ELG is the set of all f MF such that there exist c,d > 1 obeying the following condition. For all but finitely many x dom(f), c|x| f(x) d|x|. LB is the set of all f MF such that there exists d obeying the following condition. For all x dom(f), |x| d|x|. EXPN is the set of all f MF such that there exists c > 1 obeying the following condition. For all but finitely many x dom(f), c|x| f(x). BAF is the set of all f MF which can be written using 0,1,+,-,•, ,log, where x-y = max(x-y,0), x = 2 x , log(x) = floor(log(x)) if x > 0; 0 otherwise. Closure under definition by cases, using <,=, is derived in section 5.1. INF is the set of all infinite subsets of N.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 08/05/2011 for the course MATH 366 taught by Professor Joshua during the Fall '08 term at Ohio State.

### Page1 / 4

0AppA071110 - 1 APPENDIX A PRINCIPAL CLASSES OF FUNCTIONS...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online