| For every epsilon > 0, there exists a y in X such that |y-x| < epsilon. | |
| For every epsilon > 0, there exists a y in X such that 0 < |y-x| < epsilon. | |
| There exists epsilon > 0 and y in X such that 0 < |y-x| < epsilon. | |
| For every epsilon > 0 and all y in X, we have |y-x| < epsilon. | |
| For every y in X, there exists epsilon > 0 such that |y-x| < epsilon. | |
| There exists epsilon > 0 such that 0 < |y-x| < epsilon for all y in X. | |
| There exists y in X such that |y-x| < epsilon for all epsilon > 0. |