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Onetoone and ontoby nicnicman
Tags: onetoone 
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#1
Nov1812, 07:30 PM

P: 136

To me this problem doesn't seem right. Here it is:
Is the following function onetoone, onto, both, or neither? f: R→N f(x) = ceiling 2x/3 My answer: onto Although, wouldn't this function be invalid since it produces negative numbers and the set of natural numbers doesn't include negatives? Consider f(1.5) = 1. Am I misunderstanding a concept? 


#2
Nov1812, 08:38 PM

P: 332

A lot of people would consider the ceiling function to be f:R>Z.
It would be invalid to say it's f:R>N Unless you restrict R to R^{+} 


#3
Nov1812, 08:45 PM

P: 136

Well, that's the way is worded in the book, so it must be a typo. Maybe the writers meant to put Z rather than N.
Would my answer be correct if were R to Z? Thanks for the help. 


#4
Nov1812, 08:52 PM

P: 332

Onetoone and onto
Agreed.



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