Division by Zero - Can it be Done?

[Futobingoro]

If I said it, then quote it, don't make it up.

 

[Hurkyl]

It's not even right to cancel functions where they are defined, let alone where they are undefined.

e.g. arctan(tan(180)) = 0

 

[Vernon]

negative factorials and division by zero

has anyone any thoughts on approaching division by zero through negative factorials? ie if you juggle the general definition of factorials you can arrive at 1/0 = (-1)! which is the rather interesting infinity -1 x -2 x -3 x...etc
How would this fit into the Cantorian hierarchy of infinities?
It has the property that it is neither negative or positive (or both), the sign changing with each subsequent term, which maybe (?) relates to the tan 90 thing, where the negative and positive tans are impossibly equal when 1/0 is introduced.
Anyway my brain is spinning already, someone put me out of my paradoxical misery quick!

 

[bkvitha]

Futob:

Since you say that 1/0 = infinity

So is: 1/0 = 3/0

what about 1/0 – 1/0 = 3/0 – 1/0 is that equal?

Is 0/0 = 2/0?

I too would like some explanation about these statements.

 

[Nuclear on the Rocks]

Since x/0 =inf ,where x is any number then 0*inf should be x.But 0 multiplied by anything is 0.And inf multiplied is inf. Someone please resolve this paradox.

 

[matt grime]

What paradox? Every 'paradox' is based upon making some false assumption and then getting a contradiction. This is no different. Your false assumption is that things ought to behave in some way when they don't.

 

[matt grime]

How would this fit into the Cantorian hierarchy of infinities?

The infinity sign that appears in such things like this, singularities, is nothing to do with cardinals.

 

[MeJennifer]

What paradox? Every 'paradox' is based upon making some false assumption and then getting a contradiction.

So the term "false paradox" is a pleonasm?

 

[matt grime]

I should have said 'every mathematical paradox'.