The Idea of Infinity: When Mathematics Conflicts with Physics

6 min readMay 5

The simplest way to describe infinity is as an unapproachable distance. And modern mathematics, which accelerated the construction of the modern world, was born entirely from the concept of infinity.

Until the early 20th century, mathematics was divided into elementary and higher mathematics. Elementary mathematics was mathematics with addition, subtraction, multiplication, and division, that is, mathematics with four operations. On the other hand, higher mathematics was mathematics using the limit operation introduced by Augustin Cauchy in addition to the four operations. Of course, today, this kind of classification is very inadequate. I am talking about the 1800s and 1900s.

However, introducing the limit operation into mathematics as the fifth operation has greatly expanded the field of mathematics and brought solutions to many physical problems. Today, all modern science and technology products owe their existence entirely to the concept of limit.

The birth of the concept of limit in mathematics is based on the concept of infinity. In fact, the concept of infinity has existed since the beginning of human history. The great mathematicians of ancient Greece were always deep in thought about the concept of infinity. It was not until the 19th century that no one could develop a plausible definition of infinity.

In ancient times, mathematicians and philosophers dealt with the idea of infinity. Any person who had already learned to count could easily intuit that each natural number was followed by another number. In other words, the set of numbers used for counting did not have the greatest element. Because if the largest natural number existed, adding the number 1 to that number would yield a larger natural number. Thus, this set of numbers exceeded every limit, reaching infinity. So, anyone doing simple counting would inevitably encounter the concept of infinity.

However, in ancient times, mathematical knowledge had not reached a level that could resolve…


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