I just want to say implementing a mathematical function is far more convenient then using brackets. That way you can make sure anybody who gets a raise also gets to keep more, but pays more taxes at the same time. Because you will never jump a bracket which reduces your income because of higher taxes. The other benefit is, that you can easily implement a negative income tax. This would make sure that anybody who is working, has more income than people who don’t work. This would be an incentive for anybody to work what they can, even if it is very little.
You are obviously right. I always mix this up (see Bracket creep why I mix this up). But otherwise my point still stands. In this stackexchange is a graph with an example how tax brackets turn out at each income. My actual point ist, that the graph is not smooth and I don’t like that. Also there is a highest bracket, which will allows the super rich to keem growing their wealth. The fact, that super rich people are hiding their actual wealth for example via credits, is a separate issue, which obviously can’t be tackled by income tax alone.