| pokoko said: Dude. They're all artificial. In fact, some of the alternate systems were designed to make up for perceived short-comings in the classic system. I think pointing that out is completely valid. Regarding the counter-intuitive reaction a lot of people have, that's also valid and understandable. Rather, I think those who mock that reaction in a professional setting are being too narrow minded. The reason it's counter-intuitive is that one number is real while the other is not; claiming that those two numbers are the same does not feel reasonable. It's only after people realize that the "1" they're dealing with inside a system of math is not a real "1" but instead of a representation of "1", thus it can be manipulated by arbitrary rule sets. It's simply a shift of perspective that should be developed rather than expected. |
It's very understandable that people have a hard time understanding it, and it does seem counter-intuitive at first, which is why you have to try to provide proofs that are just as intuitive to understand. However when people start to deny it and claim that the math is wrong, then it's no longer so understandable, as it seems more like a knee-jerk reaction because they don't want to be bothered with understanding the concept, so denouncing it as wrong is simpler. If people don't understand it: that's completely fine. However that doesn't mean they can deny it, because it's still correct.
That said, I agree with what you have written.
