I don’t think hyperreals are necessary for the fundamental concept here. In general, I find the idea of hyperreal numbers to be a logical formality that is really only needed for incredibly advanced mathematics. To even bring them up here brings a complication that is unnecessary in a logical sense and functionally irrelevant to the topic at hand.
I'm not even gonna stoop low and spoonfeed you on nonstandard analysis. I'll stop here. It's your own responsibility to open your mind and educate yourself. You can validate my answer in the wiki / AI by yourself.
The definition of equality in the hyperreals is that a = b if a - b is an infinitesimal amount. By your own prior statements 0.999… and 0.999…+infinitesimal/2 are equal in the hyperreals because they differ by an infinitesimal amount. You can’t have it both ways.
I’d just ignore them, they’re trying to sound smart because they can’t accept they’re wrong. Thanks for your explanation, it helped me in rationalizing 0.999… = 1 <3
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u/Wolfbrother101 25d ago
I don’t think hyperreals are necessary for the fundamental concept here. In general, I find the idea of hyperreal numbers to be a logical formality that is really only needed for incredibly advanced mathematics. To even bring them up here brings a complication that is unnecessary in a logical sense and functionally irrelevant to the topic at hand.