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Division By Zero, Defined by Anonymous

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As we have all learned in our highschool math classes. Divisiion by zero is undefined. This makes many people quesy, why would something be "underfined" in something as formal as mathematics. I personally felt the world spin out of control and my death looming close by when I first heard this. Until today, when I figured out why it is "undefined".

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SOME REAL IMPORTANT STUFF

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To understand this, you have to understand positional number systems. The one that is most commonly used is Decimal. Decimal is also called base 10.Fuck the what does base 10 mean? It means there are 10 symbols available to use for counting in each position of the digit. Each position is valued exponentially. blah blah I dont feel like explaining this part look it up on wiki or something.

Base 10 commonly uses the numerals: 0,1,2,3,4,5,6,7,8,9

"It is not important what the symbols are, just that there are 10 unique symbols"

Base2 commonly uses the symbol: 1 IE: 1001010

Just a side not here, you will notice that shifting the positions left or right is equivelent to dividing/multiplying by the base in decimal.

#Example#

Base 10:

100/10 = 10

100 shifted right 1 position = 10

100*10 = 1000

100 shifted right 1 = 1000

Base 2

Decimal equivelent: 4/2 = 2

Binary: 100{4} shifted right 1 position = 10(2)

More: 1000{8} shifted right 1 position = 100(4)

So now that you understand bit shifting you can understand why division by zero is not scary at all.Dividing by zero is the same thing as bit shifting in base 0.So what the fuck is base 0???

Base 0 is a number system with no symbols, and that my friends is utterly useless. So division by zero is really just boring and useless. Thats why the ancient math mystics didn't define it.

This is also interesting:

Base 1 commonly uses the symbol 1 or 0 or anything really because it is just basic counting:

0:

1:1

2:11

3:111

4:1111

5:11111

6:111111

7:1111111

Does my definition of division as bitshifting hold for all radix? Lets hear some debate.

My appoligies 4-ch! >>1 has some serious problems, and he recently escaped my math dungeon - I've been looking everywhere for him! He's not quite done yet, as you can see above... I'm terribly sorry, I'll take him away. Go. Continue you discussions. I'm very sorry!

*turns to dungeon man*

Bad Heathcliffe! Bad! *SMACK SMACK SMACK*

ancient math mystics...what a hoot

Well, what about the problem that division by zero is just one of several forms of division that cannot be expressed as bitshifting? For example, dividing decimal 1000 by five can't be expressed as 1000 >> 0.5 or anything like that. Also, in any radix dividing by one causes problems when expressed as bitshifting.

n / 1 = n

n << 0 = n

n >> 0 = n

n/1 = n<<0

n/1 = n>>0

n/1 = n/1

n>>0 == n<<0

except of course, n>>v == n<<-v (negative v). So,

n>>0 == n>>-0

n>>-0 == n<<0 == n/1

n/1 = n>>-0

n/-1 = n>>0

n/1 = n/-1

n = -n

Wham. Actually, there are a number of ways to get n = -n when you play games with zero, so I'm not surprised people avoid it so much. Or that bitshifting doesn't happen more often outside of computational math.