Can 1/0 = universe + x ?

or alternatively,

is 1/0 > universe ?

seeking some advice as to whether 1/0 has some potential mathematical value, or whether it's just illogical

To ask what is 1/0 is to ask how many 0s make 1. But 0 multiplied by anything is 0. Some equations have no solution, and x = 1/0 is one of them.

In contrast to the equation x = 0/0, to which every number is a solution.

Except that math says that 1/0 and 0/0 are equally undefined, although I wonder if there is not a way to distinguish between these cases.

i (square root negative 1) is also imaginery but has some useful application

are there any math problems, where an imaginery number 1/0 is required to solve ?

i is such a lovely concept, and I’ve always thought 1/0 even more beautiful

Sqrt(-1) is no more imaginary than other numbers, and can exist in modular arithmetic. In mod 5, for example, -1 = 4, and 2, 3 are its square roots.

https://en.wikipedia.org/wiki/Modular_arithmetic

If u = 1/0 and i = sqrt-1
Then i is nice but u is amazing

But I do truly like the concept that all numbers are imaginery and must agree

It can be useful to topologically attach a point at infinity to the real numbers. It's called the one point compactification of the reals. Both ends of the real line wrap around and connect at the single point so that the compactification is topologically isomorphic to the circle.

What's nice about i = sqrt(-1) is that it can be attached algebraically to the reals so that the resulting complex numbers still obey the algebraic properties like the associative, commutative, and distributive laws. The complex numbers are so useful in so many ways you might almost come to think of them as the real real numbers while the Reals are just a restriction of the complex numbers to those with zero imaginary part.


The trouble with trying to algebraically attach the invention of a number, u = 1/0, to the Reals is you get something that hardly counts as a "number system". For example it would obey neither the associative nor distributive laws.

No associative law:
---------------------
If u-u = 0 and 1+u = u then

1 + ( u - u ) = 1 + 0 = 1
but
(1+u) - u = u - u = 0


No distributive law:
---------------------
u*(0+0) = u*0 = 1
but
u*0 + u*0 = 1+1 = 2


PairTheBoard

Ultimately, coherence and consistency are the gods of mathematics. Or so Plato implied.

Search youtube for "dividing by zero." There are a lot of good videos explaining why the answer is +/- infinity (iirc?).

As to your use of the word universe in your question, you should try to be more precise in your communication. Explain exactly what it is you are talking about so that there is no room for people interpreting what you are saying. If you use mumbo jumbo foo-foo type words in your questions, you will likely get answers accordingly.

interesting subject.............. and yes, apparently i (or 1/0) does have many useful applications...

1/0 is not an instance of i. Imagining a definition for 1/0 has no useful application.

Hi Ryan

Yes I was annoyed with myself for the sloppy language there.

The intention was to query whether 1/0 might be some entire universal set larger than any +/- linear infinity, as 1/0 seems to be intuitively non linear. But I might just be puffin muffins there and will check those videos.

You should think for a moment about what you mean when you say the symbol "1/0" represents a "set."

When you think about a number like 6, is that also a "set"? What do you think a "set" is?

There is value to thinking about 1/0 as a limit. You can get interesting properties out of it that way. But it's not a "number" in the algebraic sense (PTB showed how it fails some basic algebraic properties).

I really think you will want to be looking back at the topological properties. Start with the two point compactification (infinity and -infinity are two different points on opposite ends of the real line), and then imagine bringing those two distinct values together and creating a circle. Now you have just one point serving as infinity, and you have a way of transporting yourself across an "infinite" distance.

There's something interesting there, but it's not really happening the way you're thinking about it. You need to hone in that language a little bit more and get clear on what your underlying picture is.

(If you want to go beyond the traditional infinity, you might want to try transfinite numbers. But I don't think you can get there from thinking about 1/0.)

^

6 is a number

but is 0 a number ?

i haven't delved into all the philosophical and mathematical definitions of 0, i assumed that 0 was a void, null, nothingness, the absence of anything etc

and i think i just realised where i'm going wrong. i've assumed that null = 0. but null is a set theory concept and 0 is an equidistant point between -1 and 1 on a number line

i haven't watched any Youtube videos yet, but it's not hard to think of something like y = 1/0.1^x where as x approaches infinity, 1/0 approaches infinity. and x can be negative, so y can too.

another possible problem here is that i was equating a mathematical concept 1/x to a philosophical concept 'opposite of void'. probably can't get away with that either.

but perhaps 1/0 is a point in a set 1/null. i'd be cool with that as a conclusion.

What is a number, anyway?

You can think of it that way, but you'll find it a lot harder to do things with it.

"null" as a "set theory concept"? Are you using "null" to mean "the empty set"? Or something else.

What does it mean to "divide by a set"? Or "divide by a set theory concept"? You're going to have to work a bit harder in fleshing this out.

There's a very common calculus idea that you're working through here, which is that you are "approaching infinity" and it is not "equal to infinity." Both as a formal mathematical concept and an intuitive/philosophical concept, this is an extremely important idea to wrap your mind around.

This also needs more work. I would suggest starting with the known (the concept of infinity on the extended real line) before trying to work with the unknown (whatever you're trying to make 1/null mean).

https://en.wikipedia.org/wiki/Extended_real_number_line

Yes, definitely, a most important number.

That you would question it is perhaps a hangover from ancient Greek and Roman times.

https://en.wikipedia.org/wiki/0

I do have a large nose

(and yes, was thinking about Greek/Roman when I asked that question too)

And you thought you had problems making sense of infinity before...

https://en.wikipedia.org/wiki/Zeno%27s_paradoxes