In this article, we have studied the difference-difference Lotka-Volterra equations in p-adic number space and its p-adic valuation version. We pointed out that the structure of the space given by taking the ultra-discrete limit is the same as that of the p-adic valuation space.

Ultra-discrete Toda Lattice Equation -A Grandchild of Toda-, International Symposium, Advances in aoliton theory and its applications: The 30th anniversity of the Toda lattice