3月15日13時に第15期公募情報を公開いたしました。
4月1日13時より応募者登録サイトへの登録が可能です。
Information on the 15th call for applications was opened at 13:00 on 15 March.
Applicants can register on the registration website from 1 April at 13:00.
Infinity in Mathematics
We often describe a very great number as “infinity,” even though it does not necessarily mean “not finite.” For instance, even an “infinite” number of twinkling stars actually exist in finite amounts (to our knowledge, at least). Meanwhile, the infinity of mathematics really means “not finite.” For instance, natural numbers (positive numbers with no fractional portion, i.e. {1, 2, 3, …}) really do exist infinitely, and we can find many more natural numbers than the total number of stars. Due to the finiteness of our time, it is impossible to count all natural numbers one by one. We understand them through a thought experiment of infinite-time counting. How, then, can we comprehend all numbers, including fractions and decimals? We cannot count them in a regular manner, since they exist densely and not in a row. In mathematics, we often represent some object as a result of infinite repetition of some operation. However, it is controversial to say which kind of operations can be infinitely repeated to create an object with some meaning. Even the “number” itself, the most fundamental object in mathematics, requires quite abstruse procedures in order to be defined rigorously. In this seminar, I will try to give a basic explanation of the mathematical approach toward these issues. If time allows, I will discuss some topics related to my research field, differential equations.