The Importance of Zero: Uncovering its Significance

[matt grime]

Of course, without any restrictions on the interaction of the operations +,* etc, then I'm also free to declare that S=Q, and D=Qu{T}, where T is some symbol such that x/0 is defined to be T for all x (including 0) As I don't need to define an arithmetic involving T this is ok. Of course we run into problems such as what is a*b*c (note i'll pretend x*y is the same as x/y) when b*c isn't a strid number (and hence what is a*(b*c)?) but a*b is, so that (a*b)*c is allowed, even though it is "strid defined" only.

 

[strid]

when I said that it has to be defined I don't mean that you can just insert any variable as an answer. The answer we get should be on th line of numbers (including the line of complex numbers)... I hope anyone doesn't sugget creating a weird line to fit x/0...

 

[HallsofIvy]

1) Whenever I add two numbers, I'll get a defined answer.
2) Whenever I multiply two numbers, I'll get a defined answer.
3) Whenever I subtract two numbers, I'll get a defined answer.
4) Whenever I divide two numbers, I'll get a defined answer.

If, in addition, you want addition and multiplication to have "nice" properties, i.e. commutative, associative, distributive, then you want a "field" in which every member has a multiplicative inverse. It is easy to prove that the only such field contains only a single member: 0 is the only number and 0+0= 0, 0*0= 0 are the only possible operations.

 

[matt grime]

when I said that it has to be defined I don't mean that you can just insert any variable as an answer. The answer we get should be on th line of numbers (including the line of complex numbers)... I hope anyone doesn't sugget creating a weird line to fit x/0...

And exactly how does that stop the "problem" you've created? x-x=0 should be on the "line of numbers".

 

[arildno]

And what, BTW, do you mean with the "line of numbers", strid?
Is that something deep and inexplicable?
And, while you're at it, what is a "weird" line?
Is it one true line and many untrue lines?

 

[strid]

And exactly how does that stop the "problem" you've created? x-x=0 should be on the "line of numbers".

I'll have to confess that that is a little problemtaic... but for the moment, let just throw the result of x-x of the line of numbers... if something equal nothing, it doesn't exist on the line... at least for the moment... will think if I can get a better solution...

 

[Moo Of Doom]

Wow! You just "threw" 0 onto the line of numbers. Good Job!

 

[matt grime]

So, you're going to allow subtraction of numbers unless they're equal. How is this any less philosophically dubious than disallowing 1/0?

 

[strid]

Wow! You just "threw" 0 onto the line of numbers. Good Job!

I "threw" zero off, not onto, the line of numbers...

I'll let zero exist as a concept but not as a number. So when you subtract tvo equal numbers you get the concept zero, which is nothing. Similarly, if someone asks how many points exist on a line, the asnwer will be the concept infinity. So neiter infinity or zero is a "quantitiy"...

so my line of numbers would be something like this...


continue to infinitely negative big... -100... -50... -5... -1... -0,5... -0,1... -0,01... -0,0001 ... continue to negative infinitely smalll... ... ...continue to infinitely small... 0,0001... 0,01... 0,1... 0,5... 1... 5... 50... 100... continiue to infinitely big

weird to write it on computer without a timeline, but I hope you get the picture...

 

[matt grime]

But you're still not being consistent. You want the result of all subtractions (and additions) to be strid defeind, which you also claim you want to be a "strid number", so why isn't x-x=0 a strid number? And why if you're allowed to say that x-y is a binary operation, except when x=y, are we not allowed to state that x/y is a well defined binary operation except when y=0? You're just being completely inconsistent.

 

[katlpablo]

so can anyone come up with a place where the zero is good,,..

you mean one like this?

n^-1 = 1/n

n^0 = 1

n^1 = n



or


n^0 =1

 

[strid]

you mean one like this?

n^-1 = 1/n

n^0 = 1

n^1 = n



or


n^0 =1

sorry to disappoint you but n^0=1 isn't true for n=0...

0^0 is undefined and according to me (and many other) just the same as 0/0...

 

[Gokul43201]

I'm sure he meant, n \not{=}~ 0.

This thread has run its course, wot ?