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I am stuck on a math problem and urgently need help. Please, anyone who can assist, I would greatly appreciate it.
Before I pose my question, let me define the concept of a line-free cone:
A set C is called a line-free cone if it is a cone, and for every v∈C∖{0}, we have −v∉C.
Now, let n and d be two positive integers, and consider the following set:
T={(d−x,x−y):x,y∈ℕandx+y≤2nd}.The question is to find a line-free cone that contains the set T. However, I am considering the set
L={(x,y):|y|≥x−d},which contains T, but while it appears to be a cone, it does not satisfy the conditions of a cone.
If anyone could help clarify or provide insights, I would be extremely grateful.
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