Of Infinity and Beyond
What are the problems and solutions with infinity in mathematics?The concept of infinity has plagued a great many proofs, both formal and informal. I think that there are two foundational problems at play in most people’s thinking about infinity that causes issues. The first problem people have with infinity is that they treat it as if it were a single value. Because infinity is bigger than all possible natural numbers, people assume that it is bigger than any number, and therefore there is nothing beyond infinity. Therefore, people have the concept that if I have two infinities, then I still have the same number. They believe that 2 * infinity = infinity. However, using that logic can quickly lead to contradictions. This problem is exacerbated by much mathematical notation. People often will Read More ›