Division by Zero

[rcgreen]

The anomaly isn't so much with the definition of infinity, or division
by zero, but with zero itself

Zero behaves differently from other numbers. The idea of zero is synonymous with absence, so I choose to view the set of all positive integers, and zero as opposite ideas rather than considering zero to be a distinct number like 1, 2 or 3. In set theory, the idea of a null (or empty) set, is a similar idea. I emphacise that it is the number zero, not the idea, that I choose to eliminate. Presence is the opposite idea of zero and in the realm of numbers, zero reflects the absence of numbers. In otherwords, something either exists, or it doesn't. If it exists, then it has a quality that we call number associated with it, and if it doesn't exist we call this absence, zero.

http://my.tbaytel.net/forslund/zero.html

We treat zero like any other integer when we put it in an equation (because it is so useful)
but it has unusual properties that lead to strange conclusions sometimes.

[cutty]

What about -0 and +0? Have any of you guys heard of these. rcgreen has a very good point. Thanks for the link man.

Guidance...

[rapier57]

I'm no numbers guru, so what I'm adding here is pretty simple stuff. Zero is a relatively late development in numbers, and, if I'm not mistaken, isn't intended to be used in operations.

Zero, term applied to the number representing naught, denoted by the symbol 0. The fundamental arithmetic properties of the number 0 are: a + 0 = a,a - 0 = a, and a × 0 = 0, in which a is any number; and 0 ÷ b = 0, in which b is any number other than 0. Division by 0 is not defined and therefore is an inadmissible operation (See also Exponent). In the real-number system, 0 is the only number that is neither negative nor positive, and it represents the boundary between the negative and the positive numbers. This property makes 0 the natural starting point, or origin, on many scales, as on the coordinate axes and on thermometers.

In the development of written notation, a symbol for zero was evolved long after symbols for the other numbers were invented. The Babylonians used written symbols for numbers thousands of years before they invented a symbol for zero. Zero was introduced initially, not as a number to be used in computation, but as a position marker to distinguish between such numbers as 123, 1203, 1230, and 1023. The Maya, about the 1st century ad, used a small oval containing an inner arc to denote zero. About five centuries later the Hindus began to use a circle or a dot as a symbol for zero; the dot later fell into disuse. These Indian mathematicians wrote numbers in columns, and they used the zero to represent a blank column. The Hindu word for zero was œŭnya, meaning empty, or void; this word, translated and transliterated by the Arabs as sifr, is the root of the English words cipher and zero.

Microsoft® Encarta® Reference Library 2003. © 1993-2002 Microsoft Corporation. All rights reserved.

Just a little extra reference for the conversations.

The fact that zero is such a late comer can go far to explain the confusion about centuries and millenia, when they start and when they end. Like, there wasn't a year zero because they didn't have zeros then?

I didn't say that to start another argument, really, I didn't!

[darkes]

In reply to souleman, a complex number in mathematical terms is the square root of -1.

This obviously can't exist using normal numbers (a bit like infinity), as if you multiply -1 by -1 then you end up with +1. Usually this is referred to as i.

Like a lot of maths, surprisingly this does have practical uses.
How it is usually visualised is that numbers now have two dimensions, rather than one.
So instead of just 5 you can now have 5+4i for instance ...

[jjv]

Why the hell would you subtract b^2?
Then again, when you have any equation, you must simplfy it and test it.... so when you have (a+b) = b, then you HAVE to assume that a=0 or it is not a true equation... you can not have a=1 or the equation is false. so if a=0 then we go back to the original part of the equation a=b and we know that b is also equal to 0... (0+0)=0.. If you put in ANY other number for a, then you know that it is an impossible equation. You don't prove that 1=2, you prove that the teacher doesn't properl present the equation.

I believe the equation added 0 in the form of adding -b^2 to both sides of the equal sign.

Ur assumption that if (a+b)=b, then a=0...or it is not a true equation is logical; however continuing the equation without stopping to substitute a number into the equation also seems mathematically logical and perplexing. That's the fun of it.

Wonder if the original set of equations work in hex?

[souleman]

however continuing the equation without stopping to substitute a number into the equation also seems mathematically logical and perplexing.

perplexing yes...mathemattically logical..no.

Solve for X and you will see what I mean....
X = 2y
x = y+ 43x

there is always a set of possible answers. If we insert 1 (like was assumed befrore) then 1= 2 an 1= 44... you can't just randomly insert a number into the available equation, and anyone that trys is etither 1> trying to mess with your head, or 2> so ****ing stupid that they shouldn't be allowed to breath, or 3> to ignorant to ever consider teaching...

cutty> yes and no.... what is 2/1... its the number of times the denomonator can go into the numerator... or how many times can 1 go into 2.... the answer is 2...
2/-1.. is the number of times that -1 can go into 2... not really possible because -1 + -1 = -2.. -2 + -1 = -3 and on and on.... so the answer is not a true nmber... its 2i because you are using an imaginary number to devide it (either that or you say it isn't possible.

[skiddieleet]

If division by zero produces a result of infinity, then
(1/0) = infinity.
If we multiply both sides by 6, we get
0 = infinity * 1

there you wouldn't multiply both sides by 1 you would mult both by zero.
expanding that you would get 0=1/infinity.
I believe that infinity and undefined are the same because infinity is undefined. And think about it,
when you divide a number by an ever decreasing decimal you would get an ever increasing number until your decimal becomes zero which would never happen because you could always add more zero's after the decimal ex:
.01, .001, .0001 , ... , .0000000000001 , ...
I guess that's why you can't divide by zero, because it almost doesn't exist.
in limits if you take the limit of 1/x as x-->infinity you would get zero. But if you just divide 1/x as x approaches infinity you would get an ever decreasing decimal because x never actually becomes infinity.
I think math is wierd. It's just amazing to think that people thought of a whole system from scratch to explain basically everything and it actually works.

just my 4 cents.