Americans
You people have no clue what class IS, even though your society is riddled with it; Because it is part of your national myth that you don't have it.
Class is only very loosely coupled to money.
The basic class division is between the rulers and the ruled. It is defined by the position of the head of the household; If Daddy is a Congressman, then you are upper class. If he is a fry-cook, then you are lower class.
The two-class system was all that was needed in the medieval environment; If you were a part of the nobility, you had power over peasants, and were upper class; and if not, you were an expendable nobody.
The improvement in conditions for those not part of the nobility, particularly in the 18th, 19th and early 20th century, led to the division of the lower class into two parts; the working class, who could never afford luxuries, and were lucky to achieve simple subsistence; and the middle class, who lacked the power of the upper class, but who made up for this with wealth. People with disposable wealth can use that wealth to buy influence with the powerful; A middle lass man is therefore distinguished from a working class man in that he may get the attention and even assistance of his lord and master, in recognition of his financial clout.
Taken to the extreme, a 'self made man' might achieve great wealth, and great influence; If so, he joins the upper classes (although always as a lesser member - 'new money' is looked down on by 'old money' even if there is far more new money than old, and indeed even if the old money has all but vanished).
The boundary between the upper and middle classes, then, is defined by the ability to influence the people who run the country. It has little to do with wealth (although wealth can play a part); Certainly if you want the ability to mention a concern you have to the President, in person, and you know people who can make that happen for you, then you are above the middle class, even if you haven't two pennies to your name. And equally certainly, if you have sufficient wealth, you can buy a one-on-one meeting with the President by making a donation to his party or campaign, and that too makes you upper class.
Of course, as class has fuck all to do with income, so it also has fuck all to do with tax brackets, which are a completely different subject.
A sensible taxation regime would tax each dollar of income fractionally more than the last - the taxation percentage would be a smooth, non-linear function of income, with no 'brackets' at all. The problem with that is that even basic arithmetic is beyond most legislators, so such a system, no matter how sensible, will always be opposed by the majority who do not understand it.
If you want to know if somebody is in the upper class, ask "Could this person, whenever he felt the need, arrange to have half an hour of the President's (or Governor's or Prime Minister's, or King's) time, one on one, to discuss with him a concern he has about the way the country is going"? If the answer is "yes", then he is upper class - and how far up can be determined by how long it would take to get that appointment (at the pinnacle of the class system, the President/PM/King asks
you for an appointment).
If you want to know if somebody is in the working class, ask "In a typical month, could this person afford to buy all the food, clothing and shelter they need for their family to survive, and still have money left to buy luxuries, without going into debt?" If the answer is "No", then he is working class.
If someone is in neither upper nor working class, then he is middle class.
If you think class doesn't exist in the USA, ask yourself "Do people living in trailer parks have the ability (not just in principle, but in fact) to arrange a half hour of the President's time, one-on-one, to discuss their feelings on gun control"? Then ask yourself "Does anybody have that ability"? If the answers are "No", and "Yes" respectively, then you do not have a classless society.