4. Let T be a nonempty subset of the interval (0, 1). If every finite subset...

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4. Let T be a nonempty subset of the interval (0, 1). If every finite subset {x1,x2,...,n} of T (with no two of r1, 12,..., In equal) has the property that rỉ+3++ < 1, then prove that T is a countable set. (Hint: For every k E N, how many elements of T can be in k+1'k. ?) 4. Let T be a nonempty subset of the interval (0, 1). If every finite subset {x1,x2,...,n} of T (with no two of r1, 12,..., In equal) has the property that rỉ+3++ < 1, then prove that T is a countable set. (Hint: For every k E N, how many elements of T can be in k+1'k. ?)