
October 7th, 2003, 08:08 AM
#1
Division by Zero
Given previous arguments in the division by zero matter, I have opted to move this argument into this thread where it properly belongs...
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
By the same assumption, (100/0) = infinity as well.
Therefore, 0 = infinity * 100
Since both expressions are equal to zero,
infinity * 1 = infinity * 100
And cancelling the infinities, we are left with.
1=100.
This proves that division by zero does not produce infinity, if we accept that 1 does not equal 100.
If we assume that division by zero is infinity, then we must also assume that one equals one hundred. I wish you were writing my paychecks, nihil.
It can be philosophically argued whether or not infinity actually exists, and mathematically one can argue either way.
But if we let a equal infinity, then what does 1/a equal?
Let us assume that infinity + 1 = infinity.
Therefore, a + 1 = a
Now divide all terms by infinity:
(a/a) + (1/a) = (a/a)
And let (1/a) = b, so that:
(a/a) + b = (a/a)
Therefore, subtracting (a/a) from both sides,
b = 0
Or, (1/infinity) = zero.
We have now proven that (1/infinity) equals zero. If we divide one by ten, the result is 0.1. If we then multiply by ten, the result is again 1.
However, if we divide 1 by infinity, the result is zero, and anything multiplied by zero is zero. This is not a disputed fact. Division by zero is.
So,
(1/infinity) * infinity = 0
If we cancel the infinities, we are left with
1=0
And everything we know is wrong.
Abtronic, the problem in the following solution is the cancelling of (ab) where a and b are equal. This is division by zero. This was an example used to teach me the consequences of division by zero.
a = b
a^2 = ab
a^2  b^2 = ab  b^2
(a + b)(a  b) = b(a  b)
(a + b) = b
1 + 1 = 1
therefore 1 = 2.
The point: The concept of infinity is beyond the realm of human comprehension. We therefore cannot express it as an answer.
Any solutions to this paradox?
Government is like fire  a handy servant, but a dangerous master  George Washington
Government is not reason, it is not eloquence  it is force.  George Washington.
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October 7th, 2003, 08:51 AM
#2
There are a lot of assumptions in your statements Striek.
First of all since infinity is undefined we must assume that anything times infinity is infinity. So 1*infinity = infinity and so does 100* infinity. So your 1=100 assumption is off by this rule since all you are doing is saying that infinity equals infinity.
1/0 = undefined but can also be stated as infinity since in reality infinity is undefined. Take for instance a straightline graph. The slope of a line is determined by the rise/run so a slope with a rise of 1 and run of 0 would be a straight vertical line. Now we usually say that the slope is undefined but don't we really mean that it has an infinite slope?
You see infinity and undefined are used interchangeably all through math and as you go higher you will realize that they can mean the same thing. Infinity has no numerical value attached to it but we do watch trends of limits as they approach infinity. What are they really approaching? They are approaching a very large number, which we know as infinity since there's no end when it comes to counting.
Guidance...
 The mind is too beautiful to waste...
Cutty

October 7th, 2003, 09:02 AM
#3
Im just going to say 'Infinity' is a concept no human will ever truly grasp as our minds have been forever warped by the notions of 'maths' and 'time'. It is impossible to express it mathematically, and in my opinion has no practical use this side of death.
But hey, thats my view

October 7th, 2003, 09:03 AM
#4
Junior Member
Re: Division by Zero
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
0=(1/infinity) &&in reference to above.
As the denominator approaches 0, we approach infinity.
I waz also taught that division by 0 is undefined.
So what does this all mean?
Hell, I don't know. If you ever find a simple way of explaining why:
"a = b
a^2 = ab
a^2  b^2 = ab  b^2
(a + b)(a  b) = b(a  b)
(a + b) = b
1 + 1 = 1
therefore 1 = 2."
Let me know. Now, I'll be thinking about this for the next week.
Aloha,
jjv
P.S. First time I'm quoting; pls excuz if wrong as couldn't "Preview Reply"

October 7th, 2003, 09:11 AM
#5
anyhow boys i have got smthing for u check here : http://members.cox.net/mathmistakes/index.htm
guru@linux:~> who I grep i blonde I talk; cd ~; wine; talk; touch; unzip; touch; strip; gasp; finger; mount; fsck; more; yes; gasp; umount; make clean; sleep;

October 7th, 2003, 09:44 AM
#6
Junior Member
NullDevice,
Had to bookmark your reference; like the puzzles and problems.
Tnks

October 7th, 2003, 08:54 PM
#7
Member
Atomic infinity
1/0 = undefined
We don't know what it is. although mathmaticely impossible 1/0 must equal something, right?
Theoretically 1/0 has to equal something because we brought it into being (we created the equation in other words). So what does it equal? Lets look and see:
You have a 1, lets say this is one computer.
You have a 0, this is the amount of computers you possess.
How can you have 1 computer when you have none?
It is like atoms, we know atoms are made up of protons/electrons/neutrons which are made up of quarks/photons and others. But what are quarks made out of? Countinually breaking down the things in an atom till you get to something that is composed of nothing. A chemical Mankind does not know but must exist.
On the other hand, maybe you can break down atoms, maybe they can go on for infinity. Either concept is hard to grasp. the idea of something from nothing or infinite particles. Well that brainteaser should keep you thinking for a while!
\"The wise programmer is told about Tao and follows it. The average programmer is told about Tao and searches for it. The foolish programmer is told about Tao and laughs at it.
If it were not for laughter, there would be no Tao.\"

October 7th, 2003, 10:06 PM
#8
If division by zero produces a result of infinity, then
(1/0) = infinity.
False.... 1/0 = an imaginary number i, it does not = infinity... just like 2/1 = 2i, because you can't divide by a negative number.
owever, if we divide 1 by infinity, the result is zero,
False..... 1/infinity is an extreamly small number approaching 0. No matter what you say, it is just a little bit smaller then that number, but never is = 0. You can approximate it as 0, but it never truly is 0.
a^2 = ab
a^2  b^2 = ab  b^2
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.
Code:
a=b and
(a+b) = b so start with the second equation and SIMPLIFY it....
a+b = b subtract b from both sides...
abb = bb so you have
a=0 now we can return to the first equation....
a=b fill in the value for a
0=b so now we no that .....
a= 0
b = 0
we have the proper answer to the question
It is a matter of people being lazy and not following all the steps required in their math.
\"Ignorance is bliss....
but only for your enemy\"
 souleman

October 7th, 2003, 11:15 PM
#9
Dividing by zero, and infinity bring about a very fun thing in upper math classes. If you cannot devide by zero, then how close to zero CAN you divide then?
By this, I mean, as x approaches 0, what is the smallest number that is divisible before 0. There are infinite possibilities.

October 7th, 2003, 11:17 PM
#10
False.... 1/0 = an imaginary number i, it does not = infinity... just like 2/1 = 2i, because you can't divide by a negative number.
souleman just one thing I want to note to you. 2/1 is the same as 2/1 and so the answer will always be 2. I have no idea where you got your complex number from. You might want to review that.
Guidance...
 The mind is too beautiful to waste...
Cutty
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