Lower Tolerance . Preliminaries to Wroclaw Taxonomy 1 Mariusz

In this paper A, X are non empty sets, f is a partial function from [:X, X :] to R, and a is a real number. Let us note that there exists a real number which is non negative. We now state a number of propositions: (1) For every finite sequence p and for every natural number k such that k + 1 ∈ dom p and k / ∈ dom p holds k = 0. (2) Let p be a finite sequence and i, j be natural numbers. Suppose i ∈ dom p and j ∈ dom p and for every natural number k such that k ∈ dom p and k + 1 ∈ dom p holds p(k) = p(k + 1). Then p(i) = p(j).