Using divide as a 'sign' for a number

[Twinbee]

A negative number has the minus sign as its own intrinsic operator. Has anyone thought of using the divide symbol in a similar way, and has there been any attempt to standardize this throughout math?

For example (assuming / is the divide symbol):
/5 = reciprocal of 5 = 1/5 = 0.2.

It saves having to always use the "1 divided by" bit in 1/x.

One can then even use two divides to cancel each other out. Example: //5 = 5 (just like --5 = 5)

Good idea?

 

[cepheid]

People use an exponential notation instead:

1/5 = 5^-1

(5^-1)^-1 = 5

Edit: By the way, you typically have to write -(-5). If you write --5, most people won't know what you're talking about.

 

[Mark44]

People use an exponential notation instead:

1/5 = 5^-1

(5^-1)^-1 = 5

Edit: By the way, you typically have to write -(-5). If you write --5, most people won't know what you're talking about.

Unless you're writing bad C code that is attempting to predecrement a constant

 

[cepheid]

Unless you're writing bad C code that is attempting to predecrement a constant

LOL, that thought totally occurred to me as well.

 

[Twinbee]

Yes.

I still think my idea is more consistent with the idea of a negative sign (I code in C quite a bit too, so maybe my inspiration stems from there, since encoding the division sign in a number would be quite elegant in some cases).

It also means you can have stuff like:

/5 *10 = 2
10 /5 = 2 (or maybe 10*/5 = 2, and no that isn't a C comment closing tag).

So I've swapped the 'numbers' around, and achieved the same result, meaning we have commutativity just like with multiplication. We can even treat *10 = 10 (just like +10 = 10). Has nobody really thought of this crap before?

 

[Mentallic]

I'm pretty content with the way it is at the moment. We already have various ways to represent reciprocals, that being $$\frac{1}{x}$$ and $$x^{-1}$$. As for the minus operator, we don't really have many other ways to express it, so we need at least 1 way to show the negative of a number. We don't need more ways to express what we already have for reciprocals though.

As for ease of typing, $$x^{-1}$$ is pretty easy isn't it?

I wouldn't be surprised if it were implemented in some coding language, but in terms of making it standardized in mathematics, nah don't need it eh

 

[Hurkyl]

I think it's standard for the arithmetic of a wheel. But there, it's an operation in its own right (a total one, in fact) rather than being an inverse to multiplication or similar kind of thing.