Based on your response, you do not even understand the terms I've been using.
'Set of classes,' means everything per this discussion - as the discussion has been premised on the statement you made (that skin color is an indicator of class).
So when you say things like...:
"If you're trying to predict someone's behavior, distinguishing someone who makes $59,999 from someone who makes $60,000 makes no sense."
..You suggest that you either do not understand my argument, or, you do not understand what has been meant by the word "class" in this discussion.
So I'll say it again; Classes are defined by an interval on the set of natural numbers. This isn't a discussion about guessing incomes with any greater precision than those provided to us by said classes.
The data provided to us by the census bureau document is the average. Note that the "households" in the census include BOTH family and non-family households.
So, when you say things like...:
"The poverty threshold for a family of four is $22,025. Black households have a "surplus" income of $12,193. White households have a surplus income of $33,505."
...You hint that you didn't quite understand that the average provided was calculated including single-households as well as non-single households with kids. So your whole reply is a bit of a straw-man...
...But it isn't even really a good one. We are talking about race as a predictor so let us control for income and work backwards. Imagine two families, one black, the other white, both living with an income of $34,218, both with four children. Is it then your contention that the Black family is still more likely to produce a thief?
If so, I do consider your mind boggled.