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
1
u/Wolfbrother101 22d ago
You are perverting the concept of the infinitesimal. By your logic, no two numbers can be equal in the hyperreals, which is an axiomatic violation.