Much of modern mathematics is the result of centuries of wrestling with infinity. Even in school mathematics, we find the concept pops up here and there. Each time it points to some interesting part of mathematics. This is a guided tour of some of these occurrences. As usual I focus the ideas through my personal experience.
It’s a large topic, so I will make several instalments. Each begins with school mathematics, then will point into some part of the mathematics that you meet at university. These latter parts are too complex to explain in detail. I hope the reader will be content with sniffs of some of the infinitely many sub-worlds of mathematics.
Teaching Mathematics: What, When and Why 
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