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Comment by RiderOfGiraffes | Hacker News Reader

Calculus is pretty tough without infinity. Most of the theory behind fluid dynamics is pretty tough without infinity.

Not knowing that there is an unlimited number of numbers becomes a problem. Trying to do any math without allowing that between any two numbers there's another number is pretty difficult.

There are people who derive a mathematics without the axiom of infinity, but it's weird, distorted, unnatural and doesn't turn out to be as useful as often as the regular variety of math.

Feel free not to believe. Just don't expect to do much advanced math.

Oh, and if you use proof techniques in programming, such as loop invariants or transformation theory, you are using infinity, you just didn't realise it.

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Sorry for the confusion. I meant infinity, not the limit of infinity.

I have no problem with the concept of infinity in terms of limits, but that's not what this article is about. It's about the concept of infinity itself. And that is what I disagree with.

I didn't down-vote you, by the way, even though I think you are mis-guided, and probably have been badly taught. From other things you've said I think you could, if it were presented well, find the whole topic intriguing.

Because, in part, you can't have the one without the other. You can't talk about limits without having a model for infinity. They are inextricably entwined, each idea leading to the other.

It's sounds to me like you've simply been put off by loads of badly written Pop-Math articles that attempt to boggle and astound, without showing the real truths as to why the whole subject is really, really cool, and simultaneously, useful and practical.

I have no problem conceding that. Do you have anything I could read that might enlighten me on this?

Oh, perfectly reasonable but rather tough question. My thinking about teaching infinity is now at odds both with everything I've read, and how I was taught. It also depends on your own inclinations, strengths and background.

Brian Clegg's book on infinity gets good reviews, but I haven't read it. I'm thinking of starting a blog series on it, but with everything else I have on I may never really get to it.

But as I say, in your specific case it really depends on your background. If you're really interested perhaps you could email me more details on what you've studied and what you've read, and I can write some brief articles by way of reply.

Try _Everything and More: A Compact History of Infinity_ by David Foster Wallace.

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