Steve, Tom, The Kronecker delta (or Dirac delta or indicator function depending on context) appears in the technical machinery of mathematics and so does not usually show up meaningfully in the target science of the mathematical theory. The delta is a lot like a projection map (likely dual for those playing at home) in that it is useful for selecting data out of larger data, but not in any magical way. It is exactly like when we select a column in a Google doc, maybe I move the mouse over to the column and then click the mouse button. This process is internal to how I work with the data mechanistically and does not really tell me anything about the content. Seeming exceptions do arise, like when one is working with expectations in probability theory, but even these cases just make the process of 'counting' easier. The reason we perhaps wish to use something like the Iverson bracket is so that we can keep track of types. By mapping a truth value to a number, like claiming True to be 1, we can count how many people have their hands raised, say. Many people don't really concern themselves with these differences and are somehow ok with it when we write stuff like 3 * True = 3, but they are usually javascript programmers. Knuth advocates for the use of the Iverson bracket (see Concrete Mathematics) because concerning oneself with types often leads to more clear and powerful expressions of thought.
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