In fact, this is the oldest blog post archived on my website! I wrote it about 24 years ago, back when pondering on questions like this felt endlessly fascinating. What especially intrigued me at the time was how the concept of limits (the epsilon–delta definition) allows us to avoid the conceptual pitfalls often associated with infinity. Using limits, we can define and understand problems like this in a precise and rigorous manner, something that felt both elegant and incredibly satisfying.
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I've got a page about this too: https://susam.net/1.html
In fact, this is the oldest blog post archived on my website! I wrote it about 24 years ago, back when pondering on questions like this felt endlessly fascinating. What especially intrigued me at the time was how the concept of limits (the epsilon–delta definition) allows us to avoid the conceptual pitfalls often associated with infinity. Using limits, we can define and understand problems like this in a precise and rigorous manner, something that felt both elegant and incredibly satisfying.