The Way I See It, You Can Divide A Number By 0 And Get A Whole Number Answer

[LaurieAG]

Microsoft went through all this about 12 years ago.

 

If you divide by zero in the Windows 98 version a calculator and before the answer is 'error negative infinity'. In the Windows 98 version b and above calculator the answer is 'cannot divide by zero'.

[Qfwfq]

As you’ve already been informed, Zac, by almost exceptionless consensus of pro and amateur math folk alike division by zero produces not 0 but an indeterminate – that is, a number without a knowable value.

Actually it is an indeterminate form in the 0 divided by 0 case, otherwise it is infinity. It only makes sense to define these in the calculus of limits, which is not what Zac is doing.

[arkain101]

I think one way to understand this further is to look at the history of numbers and math itself.

 

Simply put. Numbers are symbols that represent quantities. The symbols we use change and have changed through out history. Zero is represented as 0. However it is entirely possible to change the symbol to something different such as a square or even as a blank space (were we to work with graph paper all the time).

 

When you write something such as 15/0 you could represent this in a different system of symbols. If we were to avoid using a symbol for zero we would get 15 /

 

This simply means the equation, is incomplete.

 

A symbol for zero is of course useful, in that it visually expresses its existence when we are dealing with a problem. Were it not there, its requirement would/could go easily unnoticed.

[maddog]

I am perplexed that 1/x as x goes to zero goes to infinity is not easily "grokkable" ! :huh:

 

There have 15 posts here (of which 10 have excellent answers).

 

I am currently not sure what math background you have so I wouldn't presume an argument by use of Calculus, etc.

 

I also note that you might accept microprocessors behave very logical. On every chip I have written code for (lots), I

have found that any division by zero is executed as an Illegal Instruction.

 

Think of is logically to divide by no groups is to not do the division. How can one do the division of a number while Not doing

it ?

 

So whether you think of it graphically, infinitessimally (Calculus), or logically, it produces a single (infinite) value.

 

Worse is to divide 0/0 - this value is Indeterminate (not even able to calculate/approximate).

 

You can approach 1/x by taking a limit as x goes to 0. Whereas x/x as x goes to 0 goes to every value (Real) simultaneously!

 

You can't even calculate that! :o

 

maddog

[IDMclean]

I am perplexed that 1/x as x goes to zero goes to infinity is not easily "grokkable" ! :huh:

 

There have 15 posts here (of which 10 have excellent answers).

 

I am currently not sure what math background you have so I wouldn't presume an argument by use of Calculus, etc.

 

I also note that you might accept microprocessors behave very logical. On every chip I have written code for (lots), I

have found that any division by zero is executed as an Illegal Instruction.

 

Think of is logically to divide by no groups is to not do the division. How can one do the division of a number while Not doing

it ?

 

So whether you think of it graphically, infinitessimally (Calculus), or logically, it produces a single (infinite) value.

 

Worse is to divide 0/0 - this value is Indeterminate (not even able to calculate/approximate).

 

You can approach 1/x by taking a limit as x goes to 0. Whereas x/x as x goes to 0 goes to every value (Real) simultaneously!

 

You can't even calculate that! :o

 

maddog

I grok the 1/x. I had never really heard about x/x tending towards every value though oddly enough in trying to come up with a system of arithmetic in which 0/0 was valid, my conclusion had been that 0/0 was the set of numbers such that it was effectively an arbitrarily valued variable.

 

If you have them, I'd like more resources on the different ways to deal with and conceptualize divide by zero problems. I have a sneaking suspicion that it could be solved in a para-consistent logic.

[Don Blazys]

0/0=V.

 

Thus, if we encounter the expression 0/0,

then even if we can't evaluate it

(by applying limits, L'Hopitals rule or some other method)

we can still substitute some variable V for it.

 

1/0=N NSEnTZ

 

It simply cannot occur in the realm of logic.

It is even more impossible than the sun coming down from the sky,

growing arms and legs, putting on a top hat, and tap dancing on Broadway!

 

Don.

[Illiad]

Dividing 15 apples into 3 baskets gives 5 groups of 3 apples

Dividing 15 apples into 4 baskets gives 4 groups of 3 apples with a remainder of 3

The remaining 3 apples then can be cut up into 4 yielding another 0.75 apples to give 3.75 apples for each basket

Dividing 15 apples into 0 groups gives 0 baskets with a remainder of 15 apples

15 apples cannot be put into 0 baskets because well, there are no baskets to hold them.

it is an impossible operation.

 

a/b = c

as b approaches infinity, c approaches 0.

However this treatment is only an approximation.

Calculus does not define a/ infinity or a/0, but only gives an approximate for it.

[freeztar]

Perhaps a better question is: Why does [math]n * 0 = 0[/math]?

[Illiad]

Perhaps a better question is: Why does [math]n * 0 = 0[/math]?

aren't they the same thing?

[Kharakov]

Perhaps a better question is: Why does [math]n * 0 = 0[/math]?

 

Yeah, read it earlier in the thread as well. That is precisely why some say that division by zero is undefined, because every number multiplied by zero = zero.

 

Like "The Skeptic" said:

10 x 0 = 0

0/0 = 10?

 

Really:

 

any number x 0 = 0

0/0 = any number although 0/0 = 0^0 = 1 by some accounts.... and 0 by others....

 

What is 0^1? What is 0^ .000001?

Both zero.. so should the answer jump to 1 at 0^0? This is discontinuous, although this really isn't that weird, considering that 0^-.00000000001 is undefined... so...

[TheBigDog]

I often find myself dividing zero when deciding where to invest the money I have saved at the end of the month. Which is a far cry better than figuring out how to take zero and divide it out into enough piles to pay all the bills.

 

Bill