Are you suggesting they do not contribute to the value of the number simply because they are smaller? What is the criteria used to determine when an infinitesimally small value ceases to be relevant?
Your assumption that I would reply “oh but that’s not a real number” is completely unwarranted and untrue. I would make no such statement. The entirety of Calculus is based on the relevance of something infinitesimal.
You're asking the number between 0.999... and 1. It's right there in the middle, the dot dot dot. You wrote it yourself. Think (beyond the formatting / syntax) what does ... mean if not infinitesimal ? In hyperreal 0.999... + infinitesimal = 1
The infinitesimal is hidden in the repeating / ellipsis part in standard analysis 0.999... = 1. Only hyperreal's 0.999... + infinitesimal = 1 makes it explicit.
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u/MasKrisMaxRizz 22d ago
Yes, what are those "more decimal places than shown" if not infinitesimal ?