The Meaning of Infinity in Mathematics

Infinity is a concept that seems to pop up everywhere. Not just in math but in science, art, love/friendship, and even sometimes religion. Infinity is a concept describing something without any bound or larger than any natural number. Infinity has an interesting history behind it, was written about, and can be very useful at times.

Infinity is the best way to describe something that goes on forever and ever. There is no such thing as a limited infinity. According to the etymological meaning of the word, “is that which has no limits.” The math definition for infinity is, a number greater than any assignable quantity or countable number. Infinity is also a symbol that looks like a sideways eight.

Just like all things, infinity has a history. It was invented by an English mathematician named John Wallis in 1657. However, it’s still unclear who the true founder of it was. The earliest account of mathematical infinity came from Zeno of Elea. He was born in 490 BCE. Zeno was a pre-Socratic Greek philosopher of southern Italy and member of the Eleatic School founded by Parmenides. Aristotle called him the inventor of the dialectic.

David Hilbert introduced the idea stated in the “Grand Hotel” in a 1924 lecture. His idea was based on if a fully occupied hotel with infinitely many rooms may still accommodate additional guests, even infinitely many of them, and this process may be repeated infinitely. Hilbert’s discussion related to infinity because if a guest came in and wanted room 1, you would need to move the person in room 2 and the people in room 2 to room 3 and so on. If this process could keep going, an infinite amount of guests would be able to stay due to an infinite amount of rooms.

In my own opinion, I believe that the use of infinity is a good thing. There is always going to be that question of, “what’s the biggest number” that little kids ask and you can easily answer with infinity. It also applies to our solar system and that there is an infinite amount of space, stars, and planets that we won’t be able to figure out, so the easiest way to explain the reasoning for unknown areas is that the sky above us goes on forever and doesn’t end. In more modern and everyday use is the infinite amount of love you promise one another when getting married. When you promise to never leave and to never stop loving each other. 

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