Does inf(X) Exist and What is Its Value?

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The discussion centers on determining the existence and value of the infimum of the set X={1/n: n∈N}. Participants suggest that the infimum can be approached by identifying it as a lower limit and emphasize the need to follow the definition of infimum. It is noted that the infimum is the greatest number that is less than any other number in the set. A proposed method involves assuming a candidate for the infimum and demonstrating that it serves as a lower bound. The conversation highlights the importance of proving that any number greater than the candidate cannot be a lower bound.
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Homework Statement


Let X={1/n: n\inN} (where N is the set of natural numbers)
i) Does inf(X) exist?
ii) What is inf(X)?


Homework Equations





The Attempt at a Solution


I think I should try to prove inf(X) exists by considering it a Lower Limit, but I don't know how to go about doing that. Any help would be appreciated!
 
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Just follow the definition.
The infiimum is the greatest number which is least than any other number in X.
 
Well, surely you can guess at what the inf might be, right? Let's say you think that x is the inf. Now, just show that x is a lower bound and if y is bigger than x, then y isn't lower bound.
 

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