Question

Consider the space R² equipped with the sunflower metric. Identify explicitly the set of points in R 2 which forms the ball B1((2, 2)) of radius 1 and centre at the point (2, 2). Provide reasons for your answer.

Answer 1

Without the specific definition of the sunflower metric, we cannot provide a precise set of points for the ball B1((2, 2)). Typically, in a Euclidean metric, it would be a circle of radius 1 centered at (2, 2), but the sunflower metric's definition is crucial to answer accurately.

Step-by-step explanation:

Given the task of identifying the set of points that forms the ball B1((2, 2)) with radius 1 and centre at point (2, 2), we need to understand the concept of the sunflower metric. Unfortunately, without a specific definition of the sunflower metric provided, we cannot give a precise answer as the term 'sunflower metric' is not a standard term in mathematics known at the time of the knowledge cutoff. However, in general terms, a metric on R² defines a way of measuring distance between two points. If we assume a usual metric, like the Euclidean metric, the set of points forming the ball of radius 1 around (2, 2) would be all points (x, y) such that the distance to (2, 2) is less than or equal to 1. This would typically be a circle centered at (2, 2) with radius 1. To answer this question precisely, the specific definition or properties of the sunflower metric needs to be provided.