A while ago I have written a post about infinity called Infinity and Beyond. At that point I haven’t encountered the concept much, but after that it appear more often in my math-life. Unfortunately it did not make things more clear for me, it just made more things hard to understand.
I have done infinite series – sums that look completely different if you take them to infinity ( I found this not very intuitive) – with the concept of convergent and divergent. Complex analysis is still a big mystery to me and I need to do more research on my own, but still here infinity for limits played a similar role as in real analysis. And them it came topology, where everything mixed in my mind with infinite dimensions. Here infinity plays an important role and from my point of view it is the base of many concepts.
The only things i enjoy a lot when it comes to infinity are fractals (but I still need to read more about the mathematics behind it) and carnality of sets (in set theory). I have talked about the last part more in the post mentioned above and it is still the math-infinity part I like the most. But I don’t consider it to be easy or intuitive, it is complicated and mixed up a lot.
These days I have read a couple of articles about infinity that made me reconsider the concept. The first one Is Infinity a Number? made me think about a lot of things: what is the concept difference between zero and infinity? why isn’t infinity considered a number? I do remember that I have read a lot about zero and how mathematicians at some point didn’t know exactly how to think of it. Moreover, at the beginning of each course the teacher makes the a remark about the set of natural numbers: for some 0 is in it, for others not. Zero is another important concept we understand poorly: it can represent nothing (if we considered it from a measure unit point of view), or we consider it the coordinate zero. But in all this, I still find the concept hard to understand in a way. You might say I think to much, but for me zero never existed in a proper way: it means something else depending on the topic we are talking about. Just like infinity sometimes. Secondly, Infinity is a beautiful concept – And it’s ruining Physics ( based on the book This Idea Must Die: Scientific Theories That Are Blocking Progress) which is about how physicist use infinity. This article made me think at the following question: in real world, does infinity exist? isn’t it just a concept we invented? In everyday life we don’t encounter this concept at all (but the duration of our life is insignificant compared to infinity – it is like 0 compared to infinity).
Many questions, different concepts, mind-blowing all of them. These are the flavor of mathematics and philosophy. What is your theory about infinity?
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