The Intuition behind Infinity— Stepping into Cantor’s Paradise
What is infinity? Are all infinities the same? Does it even matter in the real world? These are some of the questions that were roaming around the mind of Georg Cantor back in the 19th century. But even before Cantor, infinity has always played a crucial role in mathematics and, more generally, in the development of philosophy. Let’s put what we think we know aside for a moment, and dive into the abyss of the concept of infinity together.
No one shall expel us from the paradise that Cantor has created for us — David Hilbert
Infinity — An Elusive Ghost
From the dawn of time, the human spirit was attracted to things that it couldn't grasp on an intuitive level. Even the most primitive human knew what the number ‘five’ represented. He could just look at his hand and see how many fingers he had.
But what about infinity? This is certainly more challenging to describe since it is not exactly present in our everyday lives.
On an abstract level, infinity indicates the quality of being never-ending. An unlimited extent of something; space, time, numbers, you name it. And frankly, this is as close to a definition as we can get. Infinity is not a number, it is not a…
