So you’ve exhausted rational proof, and you still encounter opposition.
What then do we conclude? You’ve correctly identified that the cause is mathematical ignorance, likely more within the context of flawed education standards than individual fault. The expected consequence of this cause is irrational opposition - as is logically consistent with the that fact that your opposition is against exhaustive rational proof.
This is why I’ve identified that the only valid way to approach this thread is psychological.
This is much to the frustration of the irrational opposition, but the alternative is tedious repetition. You keep repeating all the rational ways the prove your position from a point of knowledge and experience, and they keep repeating all the irrational ways that they think prove their position from a point of ignorance.
It’s an interesting question to ask - why do people dig their heels in, even when they’re wrestling with a topic that they know they’re weak at, and dealing with people who genuinely do know what they’re talking about?
Obviously the low-hanging fruit for them is to get on their high horse and protest that this is a rational debate and it should only deal with the topic directly - even though I’ve just rationally shown that this is not the case, and that dealing only with the topic directly is the whole problem.
From what I can tell so far, there’s not much more going on than the good old Dunning-Kruger effect, along with plenty of cognitive biases and logical fallacies - notably “confirmation bias” and “moving the goalposts”. There’s a lot of forgetting rational arguments that already countered irrational positions, denying that they ever existed, or insisting that they’re irrelevant - anything to avoid the cognitive dissonance of honest introspection.
It’s a psychologically difficult process to admit you’re wrong or not in the position you thought you were, that you wanted to see yourself as being in. People want to hear and remember things that support their position and make them feel validated, special and competent - especially if they don’t feel that way overall in their normal life. It becomes a socially detrimental force when people begin to construct their own identity and a sense of purpose around topics in which they lack sufficient expertise, emotionally investing in them and feeling personally attacked when people challenge your cause. This is especially so when there are others around in the same fragile state of mind, looking for someone with a sense of confidence who is defying a way of thinking that they’re weak at - this vicariously soothes their insecurities and only bolsters yet another movement against rationality, leaving experts such as yourself in a state of confusion about how you’re supposed to deal with what’s going on. It’s truly toxic.
So of course they’ll attack your mathematical competence as a weakness rather than admit their mathematical incompetence is their weakness.
We see it in politics all the time - e.g. “if someone sides with something you don’t agree with, they’ve been brainwashed by them.” It’s taken as “the” (necessary) conclusion, when it’s just “a” possible (sufficient) conclusion that might hold or might not: abductive reasoning. In some cases it’s actually going to be because one person understands something that the other doesn’t - yet it’s so much easier and lazier to simply trust your own prejudices and assume the other person is the ignorant one. Confirmation bias so often clouds all the evidence against this, and over-emphasises all the memorable moments of victory when it’s at least seemed like you were right.
It would appear as though all this “extra baggage” that you’re talking about is simply, or at least largely a result of the above. Mathematically challenged people want to believe that it’s maths that is at fault rather than them.
To this end they see as far as they want to see and no further.
It’s easy to note “0.9 < 1”, “0.99 < 1”, and that since this pattern continues, it must continue indefinitely under all possible circumstances. One simply neglects the key property of infinity that changes this finite pattern, and voila - it can seem as though you were right all along.
Yet the obvious truth that you pointed out is essentially undeniably tautological - math and only math defines all the notations involved in the topic, and in like manner math completes how they equal each other.
That’s as far as rationality “need” go, even though all the proofs you understand and can expertly articulate can extend this rationality far further - there’s only one answer to objections to this: they’re necessarily irrational. And the reason why this irrationality exists is as I’ve just explained.
The only issue left to resolve in this thread is how to resolve irrationality. Demonstrably the answer to this is not simply “rationality” - as the irrational response to rationality is the whole problem to begin with.