What are diam and k-cell ?
Here is a problem I came up with that is extremely easy, but when I posted it on another forum it took a while for someone to answer and the answer was much more complex than what was needed. Let's see if MHF has better mathematicians....I have faith!
Question: Find the largest in such that every k-cell (denoted ) has finitely many points such that . Prove that this is the largest .
In a metric space
,
that is it is the diameter of the set (where is the "distance from to , that is is the metric).
Now my guess is that and are supposed to be the same thing, but who am I to say.
What supprises me is that with the level of clarity of the statement of this problem Mathstud28 got any solutions let alone one correct but more complicated ( ) than what he thought was needed.
CB