# 1 divided by zero

## 1 divided by zero=?

• ### Other(explain):

• Total voters
13
• Poll closed .
In my mind it isn't infinite because it never even approaches it. I understand how things that approach a certain point, for example how a 1/x graph gets close to the intercepts, but never touches, then yeah at infinite it will be touching, but this never gets anywhere, so....thats my point.

arildno
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fdarkangel said:
are you sure you've read my post?
Yes, I've read it. It is irrelevant to the fact that 1/0 cannot be defined in the real number system.
(Which follows from the fact that given any real number "a", a*0=0)

arildno said:
It is irrelevant to the fact that 1/0 cannot be defined in the real number system.
really?

fdarkangel said:
steps of division are, you subtract the divisior from the divdend as long as there's something remaining dividend, ie it hits 0. for each exact subtraction, add 1 to the counter (ie, division). (i'm not covering the details for fractional parts, since my purpose in telling this is to remind the definition)

so, applying this definition to 1/0: subtract 0 from 1 as long as you have a non-0, and add 1 to the counter each time. now, if you do this for 1/0, what's your counter?
can you see the definition now?

moose said:
In my mind it isn't infinite because it never even approaches it. I understand how things that approach a certain point, for example how a 1/x graph gets close to the intercepts, but never touches, then yeah at infinite it will be touching, but this never gets anywhere, so....thats my point.
What point is that? In this particular case we are not concerned with limits. We are stating that 1/0 (as a real number) is not defined for the reasons which have been shown above by jcsd. There are defined properties for the real numbers ( or fields in the more general sense) which we hold true. What has been shown is that if a number such as 1/0 were to exist, then it would contradict those properties. Hence we define that no such number can exist.

Last edited:
fdarkangel said:
really?

can you see the definition now?
Your definition of division is not the same as the definition of division on the real numbers.

master_coda said:
Your definition of division is not the same as the definition of division on the real numbers.
i guess you're implying the irrational numbers. i was not willing to expand the algoritm for non-integer results. i have never given any irrational number input. if you mean the non-integer results.. well, here it goes:

let A and B two reel numbers. subtract B from A until A is bigger or equal to zero, and add 1 to the division at each step. after this process, if A is negative, undo the one step. multiply A with 10 (or what ever the step is) and add $$10^{-1}$$ to the result after each subraction. repeat these steps until A=0, and decrement the power of 10 (to generalize, base) by 1.

however, i'd like to point that the original question is integer-wise, and this definition was uncessary.

fdarkangel said:
i guess you're implying the irrational numbers. i was not willing to expand the algoritm for non-integer results. i have never given any irrational number input. if you mean the non-integer results.. well, here it goes:

let A and B two reel numbers. subtract B from A until A is bigger or equal to zero, and add 1 to the division at each step. after this process, if A is negative, undo the one step. multiply A with 10 (or what ever the step is) and add $$10^{-1}$$ to the result after each subraction. repeat these steps until A=0, and decrement the power of 10 (to generalize, base) by 1.

however, i'd like to point that the original question is integer-wise, and this definition was uncessary.
But you attempted to extend the algorithm to try and divide by zero. Once you do that, the algorithm is no longer giving the same results as real number division.

it does, for integer results.
i expanded the algorithm to generalize. basics of both division methods are same. the initial explanations i made about 1/0 and 0/0 are still correct. please don't be so pedantic, the interger-only algorithm is consistent and sufficient enough to explain 1/0.

chroot
Staff Emeritus
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fdarkangel,

Again, you are wrong. Master_coda is correct. Your algorithm is, basically, junk.

Either way, this thread is just a rehash of many other similar threads here. We don't need another thread with the same arguments from the same people.