Browsing by Author "Mayila, Shega"

Now showing 1 - 3 of 3
  • Thumbnail Image
    Item
    Analysis and investigation of logical flaw of Zeno’s Achilles-Tortoise paradox
    (Informa UK Limited, 2024) Mayila, Shega; Mpimbo, Marco; Rugeihyamu, Sylvester; Hari M. Srivastava
    In this paper, we analyze the Achilles-Tortoise paradox, which denies the overtaking of the slowest runner (Tortoise) by the quickest runner (Achilles) because the pursuer must first reach the point whence the pursued started, so the slower must always hold the lead. The paradox translates into a requirement for the quicker to complete one by one an infinite sequence of distinct runs in a finite time to overtake the slower. This feat is impossible because the infinite sequence of distances contains no final distance to run, and the time to complete such a feat is not enough. However, we know better that in a race, the quickest always overtakes the slowest. Then why does the argument say otherwise? There should be logical flaws in its argumentation. Therefore, after an analysis of the paradox, we investigate the existence of such a flaw that exists in the argument itself or in the inferences its premises make. In addition to this, we present the new mathematical solution based on open balls in real Euclidean space, which shows that only a finite number of runs are needed by the quickest to overtake the slowest.
  • Thumbnail Image
    Item
    Analysis and investigation of logical flaw of Zeno’s Achilles-Tortoise paradox
    (Informa UK Limited, 2024-03-16) Mayila, Shega; Mpimbo, Marco; Rugeihyamu, Sylvester; Hari M. Srivastava
    In this paper, we analyze the Achilles-Tortoise paradox, which denies the overtaking of the slowest runner (Tortoise) by the quickest runner (Achilles) because the pursuer must first reach the point whence the pursued started, so the slower must always hold the lead. The paradox translates into a requirement for the quicker to complete one by one an infinite sequence of distinct runs in a finite time to overtake the slower. This feat is impossible because the infinite sequence of distances contains no final distance to run, and the time to complete such a feat is not enough. However, we know better that in a race, the quickest always overtakes the slowest. Then why does the argument say otherwise? There should be logical flaws in its argumentation. Therefore, after an analysis of the paradox, we investigate the existence of such a flaw that exists in the argument itself or in the inferences its premises make. In addition to this, we present the new mathematical solution based on open balls in real Euclidean space, which shows that only a finite number of runs are needed by the quickest to overtake the slowest.
  • Thumbnail Image
    Item
    On a nation as a topological space
    (Taylor & Francis, 2023) Mayila, Shega; Mpimbo, Marco; Rugeihyamu, Sylvester
    This paper introduces point-set topology into international interactions. Nations are sets of people who interact if there is a well-defined function between them. To do all these, we need to have the structure that describes how such nations interact. This calls for a topology. The kind of topology we construct in this perspective is made up by decision spaces. We first begin by developing a mathematical representation of a decision space, and use such spaces to develop a topology on a nation. Subsequently, we revisit some properties of the interior, closure, limit, and boundary points with respect to this topology and the new concept of ϕ - proximity. Finally, we define and develop ϕ - connectedness of subspaces of a nation.