The Correspondence Between n-dimensional Euclidean Space and the Product of n Real Lines

The articles [2], [6], [10], [4], [7], [18], [8], [13], [1], [3], [5], [15], [16], [17], [21], [22], [9], [19], [20], [11], [14], and [12] provide the notation and terminology for this paper. Let F be a set. We introduce F is n-long as a synonym of F is empty. We introduce F is finite sequence-membered as an antonym of F is empty. We introduce F is quasi-prebasis as an antonym of F is empty. We introduce F is e-quasi-basis as an antonym of F is empty. For simplicity, we use the following convention: x, y are sets, i, n are natural numbers, r, s are real numbers, and f1, f2 are n-long real-valued finite sequences. Let s be a real number and let r be a non positive real number. One can verify the following observations: ∗ ]s− r, s+ r[ is empty, ∗ [s− r, s+ r[ is empty, and ∗ ]s− r, s+ r] is empty. Let s be a real number and let r be a negative real number. Observe that [s− r, s+ r] is empty.