I hear you CAN divide by zero...?

Question

I heard somewhere that on some ultra high level DesCartes / Gaussian / Fourier / Eigen Valueblahblah / Chuck Norris mathematical level that TECHNICALLY you can divide by zero, and wanted to know where this is possible. I recall that it might have also had something to do with an algorithm that the number 'one' does not exist. If you ask me, I just think it proves how flawed the decimal-based number system is... Any ideas???

Answer 1

You cant divide by zero.

Straight arithmetic operation... n/0... not possible

However, when taking the limit of a fraction n/a... where the denominator approaches 0... is possible.

Look up limits... and their evaluations

Answer 2

The Base 10 number system is not "flawed" in the sense that there is something wrong with it. The "rules" were set up to handle certain calculations easily. If you are dealing with computers, you often use Base 2 and Base 16, because it is easier than Base 10 for some things.

You have to remember that the point of ANY branch of mathematics (and there are LOTS) is to provide a compact, orderly system of rules in order to make sense of some physical reality. But the physical reality never changes, only your ability to calculate and quantify it.

You are probably thinking of limits. If you have 1/x, as x approaches 0, the expression grows very large. For instance, 1/1 = 1, 1/(0.5) = 2, 1/(0.1) = 10, 1/(0.001) = 100, and so on. As the denominator gets smaller, the whole expression gets larger.

So TECHNICALLY, if you "stuck a zero in there", you would get "infinity". But this is not REALLY dividing by zero, because "infinity" is not a specific number like 1 or 2 or 10 or 100 is. We say "the limit approaches zero", and "the expression APPROACHES (but never reaches) infinity". You may think this is splitting hairs, but it is not. The decimal system does not break down here; you still can't divide by zero. Why? Because 0 times X is ALWAYS zero, no matter what number X is.

Answer 3

Sometimes, with limits, an answer can be found that seems to divide by zero. A simple example:

x/x as x -> 0.

Any number divided by itself equals 1.

with x approaching 0
.000000000000000001/
.000000000000000001 = 1, while it may be undefined at 0.
A million leading zeros on the top and the bottom would not change the answer. So,

While we mark a "hole" on a graph. The answer is :
the limit of x/x as x approaches zero is 1.


This is not a flaw of the decimal system. Making the jump to limits and derivatives held mathematics up 1500 years.

Answer 4

Think of it like dividing a pie. For example the fraction 1/4. That means you divide the pie into 4 equal pieces and just take one. Now look at the fraction 1/0. Can you divide none of a pie into one piece? Its not possible to divide by zero.

Answer 5

Sure you can -- provided you're in the finite field with one element, where 1=0. Otherwise, you can't.

To divide by something is to multiply by its reciprocal. That definition always holds.

The reciprocal of X is the thing that, when you multiply it by X, gives 1. But it is also the case that 0 multiplied by anything gives 0. So unless 0=1, you can't divide by 0.

Answer 6

Lets try it, Assume you can divide by zero.

1) X=Y ; set X=Y
2) X^2=XY ; Multiply both sides by X
3) X^2-Y^2=XY-Y^2 ; Subtract Y^2 from both sides
4) (X+Y)(X-Y)=Y(X-Y) ; Factor
5) X+Y=Y ; Cancel out (X-Y) term*
6) 2Y=Y ; Substitute X for Y, by equation 1
7) 2=1 ; Divide both sides by Y

step 7 shows that 2=1 which is a contradiction, so our assumption was wrong, we can not divide by zero in step 5.

Answer 7

We still pretend it is a free country, so go ahead, Divide by zero, don't let the fact that different limiting factions are separated by two times infinity.

Answer 8

Nah, still can't divide by zero. One definitely does exist because we can prove that there is one me (I hope...), one can of Pepsi on my table...so that's how we throw out that algorithm. Dividing by zero would require that it would actually divide it. If you divide something by zero, it won't go in because you're putting nothing into something and it's just a waste of time. You're putting many things into groups of however many you're dividing by. 34 bananas divided by 2 equals 17 groups of two bananas. But if you try to divide those by zero, you can't have any groups of no bananas because you still have bananas. I have officially confused myself. But I think it works.

Answer 9

You can't actually divide by zero, but in first-semester calculus, you can get awfully close. You might think of differentiation as dividing something very close to zero by something else very close to zero...

Answer 10

its not actually zero but a number too small that approaches zero (like 0.000000000001).. if you divide any number by this too small number, you will get a infinity answer-- too large to quantify..