Infinity Reloaded

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? 

Thank you for your help and support. All your help means a lot to me. Thank you for reading. You can find me on Facebook, Tumblr,  Google+,   Twitter  and  Instagram. Don’t forget that maths is everywhere! Enjoy the weekend! ^_^ 

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9 thoughts on “Infinity Reloaded

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      1. In the future, I may write more about infinity in my blog. However, since many of my readers prefer easier math, I can’t write about it in more details for now :). If you want good resources regarding the subject of infinity, then nothing beats books. Here’s some of my recommendations;

        Uses of Infinity by Leo Zippin – This is a good introductory text for infinity. You only need to have a firm ground in high school level math to understand this book. One of the most interesting section of the book js his use of geometry to explain limits instead of using analytical methodologies common in calculus.

        Gödel, Escher, Bach: An Eternal Golden Braid by Douglas Hofstadter – Another great book 🙂

        The Mystery of the Aleph: Mathematics, the Kabbalah, and the Search for Infinity by Amir D. Aczel – This is a must read if you are interested in infinity. This book details the development of the concept of infinity in mathematics (and mainly about the works of Cantor)

        Those are just some of the books that are really good but of course there are many others out there as well. If you want some advanced stuff, then don’t forget to check out Ramanujan’s works on Ramanujan’s notebooks. His works on infinity are very underrated IMO.

        On Youtube, there are also a lot of excellent videos regarding the subject. For example, you may check out this video about Zeno’s Paradox by Numberphile

        Btw, if you are having difficulties with complex analysis, then consider reading Basic Complex Analysis by Marsden and Hoffman. Although it’s a bit old (1998), it is one of the best introductory books for complex analysis that I have ever seen. Well there’s also Complex Analysis by Freitag and Busam…

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      2. There is so much… Thank you very much for your help. Sometimes I find really hard to just Google what I want to read and find the right thing. Thanks a lot. I will try to find and read as much as possible.

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      3. Yes, many articles on the web lacks depth if you know whatI mean. They are good for introductory purposes, but if you want to learn to learn a subject in more detail, books are still the best.

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  1. I am as hypnotized by infinity and zero as you are it seems… 🙂 Funnily enough I bought “This Idea Must Die” (I love Edge.org – and John Brockman is an excellent curator!) but I don’t remember the essay about how Infinity is harming science – though a priori I agree with the premise. I’m convinced the human mind reasons only in terms of ‘sameness’ and ‘difference’ (where in my sense ‘difference’ is just a ‘different kind of sameness’), so that both ‘infinity’ and ‘zero’ mean ‘sameness’ to a brain and nothing more… But that’s where I’m struggling with my current project which I’ve come to call a “trivialistic” paraconsistent logic… and I’m using what I call ‘adjacency maps’ to represent Things (in the most general sense)… it all makes ‘sense’, but unfortunately, it is turning-out to be more ‘actually trivial’ than ‘trivialistic’ 😦 *whimper*… such goes the poem of Pangur Ban: “… ‘Gainst the wall of Knowledge, I, all my little wisdom try…” (I love this poem! I think you might too. Full version here: https://www.ling.upenn.edu/~beatrice/pangur-ban.html)

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    1. Sometimes I get the same feeling about some of my projects… they become to trivial at some point, but never give up… I think great things come from trivial ones ^_^
      Also, the poem is great (never been a poem fan). My favorite lines: “O what gladness do I prove/When I solve the doubts I love!” So beautiful. Thank you 🙂

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