A Third Math Sign - not just positive or negative

I was thinking about a random thing the other week. We have positive and negative signs in widespread and ubiquitous use in mathematics. What if we had a third sign?

The number line would look like the one in the picture. It's not even a line anymore.

Since I am absolutely dumbfounded as to how even the basic operations would play out in this type of system (although I have a rough idea for addition and subtraction), and nor do I know what the possible applications for a redundant sign could be, I'm just putting this here.

Got ideas? Fire away.

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3D systems are widely used, for example when times comes into the calculations.

I just wonder what the sense behind a third sign would be...

nutsandbolts_64 (author)  Downunder35m3 years ago

The thing in the picture isn't a 3D graph. It exists only on one plane.

My wondering of what a third sign could be used for is exactly why I posted it here.

You cannot just say "let's add a third sign," but not define what it means. Interestingly enough, the above graph is exactly how you would "project" a 3D graph when it's presented in 2D...

So if the above data "exists only on one plane," then one of the problems with this proposition is that all the data points on the above graph can be adequately described in two dimensions. Add another dimension? Then it becomes a 3D graph. More? Difficult to visualize, but they exist.

You also should remember that "zero" can be an arbitrary reference. There's no particular reason why multiple axes have to meet at zero (turn into CNBC market coverage for examples).

You can call it whatever you want, but in this plot, the other two axes are _not_ "positive" and "negative." Each axis measures numerically positive values, but the three quantities are different, and generally orthogonal.

Besides the term "ternary plot" I already mentioned, you might also look up "barycentric plot", where each plotted point corresponds to a two-dimensional "average" of the three input values.

Positive and negative numbers exist in a single line. Numbers at right angles to them are the imaginary numbers. Numbers composed of a real and imaginary number are called complex numbers.

Complex numbers are extremely useful in engineering and physics for representing lots of entities.

caitlinsdad3 years ago

Would that be the absolute value numbers? There is notation for that already.

kelseymh3 years ago

This is called a "ternary plot." Two specific examples are the "color triangle" and "Dalitz plot."