Texts: x, y, z ∈ ℝ
X: ∀ x ∈ ℝ, ∃ y ∈ ℝ, ∃ z ∈ ℝ, 1 > |x - y| > |x - z| > 0
The statement above means:
For every number x, there exists a number y that is closer to it than one, and another number z that is even closer to x than y. All |x - y|, |y - z|, and |x - z| are small absolute values. |x - y| and |x - z| can be made small. We can choose x, y, z so that |x - y| and |x - z| can be smaller than 1. There exist y and z that are close to a given number x. Not well defined. There exist three numbers x, y, z that are not equal. For every number x, there exists y > x and z > y. For every number x, there exists a number y that is closer to it than one, and another number z that is even closer to x than y. Both y and z are not equal to x. None of the answers given is correct.