Zero; a very powerful machine in mathematics but it needs better treatment.

Well, what I *really* want to see is not so much a handedness.. perhaps _something_ capable of showing where it fits in the greater context of where it is used and what it is used for.

I suppose what I’m thinking of is to bring in a distinction of purpose. Zero has multiple uses and is quite powerful.

It is used as a placeholder.
It is used as a marker of “Start” for the number line.
It is considered the lowest Even number.
It is used as a marker for “Success” in balancing systems (such as economics)
It obliterates identity entirely; a number loses its positiveness and negativeness and its quantity.
Conceptually, it’s the “empty bucket”.
Conceptually, it’s non-movement or stillness or balance.
Conceptually, it’s potential as it either *could have once* represented something or it *could* in the future represent something.
Conceptually, it’s absence.
Conceptually, it’s “I can’t know” of a very strong form.

This is off the top of my head; please correct me if I’m mistaken in these things.

But it seems to me that, perhaps zero serves too many purposes without distinction, leading to confusion.

I have a similar issue with the modern concept of impetus versus the Newtonian usage. Impetus that is external or internal are considered the same now; both external; but in Newton’s time and before, Impetus was a pretty hot topic.

But that’s with Science. At least in mathematics, the Axiom would be the intrinsic impetus and the Proof would be the extrinsic impetus, in my viewpoint creating a marvelous engine which drives mathematics both from without and within.

Yeah, I tend to conceptually analogize to machines.

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