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[cody dooderson]

I have only seen them inside of summations, Σs*,* but I'm sure they are
used elsewhere. They are used like a filter.  For instance, if you want to
sum weights of butterflies in an insect database you would say "for every
insect in X, if it is a butterfly then add it's weight to the sum". When it
gets translated into an equation, the part "if its a butterfly" gets turned
into a Kronecker delta function where it outputs 1 when it is a
butterfly and 0 otherwise.
So in some sort of pseudo equation, it might look like  y=Σ*_of_i_in_X(
Kron_delta( Label(i), "butterfly") * Weight(i) )*

I hope this doesn't muddy the water too much,
Cody Smith


On Mon, Jun 8, 2020 at 4:00 PM Frank Wimberly <wimberly3 at gmail.com> wrote:

> 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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