Demosthenes
2008-02-25, 05:29 PM
WetWired, in an earlier thread you stated that omega was the largest integer. I didn't think such a quantity existed. The reason I bring this up now is because of a question in one of my classes.
If we have a potential vector space with addition of two vectors defined as x+y = max(x, y) then according to my understanding of the number system this would not constitute a vector space. The reason being is that there is no singular 0 vector for the entire vector space, meaning there is no value of y I can think of where max(x,y) will always give x because y can always be x-k. However, if a number such as omega exists, then negative omega should satisfy the conditions and constitute a 0 vector. I was just wondering if you could clarify, since I was always taught that the idea of the "largest integer" is non-sensical.
If we have a potential vector space with addition of two vectors defined as x+y = max(x, y) then according to my understanding of the number system this would not constitute a vector space. The reason being is that there is no singular 0 vector for the entire vector space, meaning there is no value of y I can think of where max(x,y) will always give x because y can always be x-k. However, if a number such as omega exists, then negative omega should satisfy the conditions and constitute a 0 vector. I was just wondering if you could clarify, since I was always taught that the idea of the "largest integer" is non-sensical.