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[Frank Wimberly]

OK.  The Kronecker delta on a set A is a function or set of ordered pairs.
The arguments of the function are ordered pairs of the elements of A.  The
elements of the function are defined by <<x,y>, z> where x and y are
elements of A and z is in {0, 1}.  In other words the domain of the
Kronecker delta is the set of ordered pairs of elements of A and it's range
is the set {0, 1} and the function is evaluated as delta(x, x) = 1 for all
x and delta(x, y) = 0 if x != y.

Is that better?

I stand by my original post


---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505

505 670-9918
Santa Fe, NM

On Mon, Jun 8, 2020, 3:33 PM Jon Zingale <jonzingale at gmail.com> wrote:

> 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.
>
> Jon
>
>
>
> --
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