Division by 0

[CrazyCat]

Not too long ago, an idea struck me. It concerned division by 0. Now, one way to think about division is how may times can the divisor go into the dividend. For example, if you divide 12 by 4, the answer is 3 because 4 can go into 12 3 times. So I thought, if you encounter a problem such as 6 divided by 0, the answer would be ∞ since 0 can go into 6 an infinite amount of times. So, in other words, x/0 = ∞. Now I know this may be completely incorrect, but I thought I'd share it with you guys anyw- *Black hole forms* 

OH SHI-*Gets sucked into black hole*

[Ares the Ram]

welp, in order for something to be infinite, it has to be doable over and over again without stopping. Imagine a 6" wide board going into a hole in a wall. The hole is 3" wide, so if you could push it in, you'd lose half of the board, or .5, the same amount as 3/6, and vise versa. now 6/0, 6" wide board, and 0" wide hole. 0" wide hole means there is no hole, and thus you cannot push the board into the wall, making the equation impossible. 0/6, 0" wide board and 6" wide hole. You cannot push nothing into the hole, and thus is also impossible. 

[CrazyCat]

Welp, now that I reread my post and your reply, I realize that there might have been some miscommunication (My bad ). What I meant by how many times the divisor goes into the dividend was how many times you have to add the divisor to itself to get to the dividend. Let's use the 12/4 example again. To get to 12, you have to add 4 to itself 3 times (4 + 4 + 4 = 12). Now, in a problem such as 6/0, you could add 0 to itself over and over (0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0...)  again without stopping (definition of infinity) and you wouldn't ever get to 6. Or 1 for that matter. I understand what you're getting at though.

[Nrein]

To kinda of build off, even if it can't be infinite, wouldn't it just be zero? o.o
Because 6/0, six goes into zero, zero times. 0/6, zero goes into six, zero times.
Just more trouble to add to the equation x3

[Gelidus]

It's basic calculus

  lim    8/x = ∞
x-->0  

It's one of the first things you learn when you take the class

[CrazyCat]

It's basic calculus

  lim    8/x = ∞
x-->0  

It's one of the first things you learn when you take the class

Oh, cool Haven't taken any calculus class so I didn't know that. Also, what does "lim" mean? Like I said, no calculus background so I don't know this stuff.

[Gelidus]

It means the limit. basically what that means is you take what ever variable (x in this case) and you divide it by a number that is closer and closer to the limit. In this case, the limit is zero, so what we would do is divide by .001, than by .00001, than by .00000001 and so on and so forth. Whatever those numbers approach, is the limit of the equation. In this case, the smaller the number we divide by, the greater the solution becomes, until finally we divide my such a small number, that the solution become exceedingly large. We can only conclude that the solution is infinity

[CrazyCat]

Neato

So, I'm pretty much wrong, right? 

[Gelidus]

Actually you were completely right  

although I should mention, It can also be true that lim   8/x = -∞
                                                                        x-->0

Why is this? well if you do the same thing, but apporach it from the other direction, we find that it will equal its negative counter-part. If you divide by -.001, then by -.000001 and so on and so forth, you'll reach negative infinity instead of positive infinity.

Are you enjoying your calculus lesson

[CrazyCat]

Oh, sweet!

Also, I think I've had enough calculus for today. It's nearing midnight and my brain needs rest.

[Blackout]

Basically, depending on which way you approach it, you can end up with 0 or ∞ (or -∞), both of which are just as "wrong" as well as "right" as the other.

[CrazyCat]

To kinda of build off, even if it can't be infinite, wouldn't it just be zero? o.o
Because 6/0, six goes into zero, zero times. 0/6, zero goes into six, zero times.
Just more trouble to add to the equation x3

You're doing it wrong Nic. (Ish okay though. We all make mistakes)

In a division written in that format, the number on the right always goes into the number on the left. In 6/0, it is always 0 that goes into 6, not the other way around. For that to happen, the problem would have to be written as 0/6. Hope that helped.

Post Merge: August 01, 2011, 04:44:16 AM

Basically, depending on which way you approach it, you can end up with 0 or ∞ (or -∞), both of which are just as "wrong" as well as "right" as the other.

How would x/0 = 0? Can you please explain?

[Nrein]

You're doing it wrong Nic. (Ish okay though. We all make mistakes)

There's a reason I added "Just adding more trouble." I know I was doing it wrong x3 I'm fantastical at math, except Calc I hate~ it v.v, and I was just pocking fun at it since I'll never see it again >=3

[CrazyCat]

You're doing it wrong Nic. (Ish okay though. We all make mistakes)

There's a reason I added "Just adding more trouble." I know I was doing it wrong x3 I'm fantastical at math, except Calc I hate~ it v.v, and I was just pocking fun at it since I'll never see it again >=3

Ohh, my bad xD

Also, I thought the "Just adding more trouble" was because what you said was gonna add to the confusion.

[Nrein]

It just did >=3