Originally posted by smithjustinb
Mathematic understanding is flawed due to its one and only uncertainty that is to divide any number(n) by zero. In that operation, the answer is
determined as undefined
Your understanding of division by zero is unfortunately misunderstood. Instead of attempting to divide a number by zero and then immediately
pronouncing that you get an ambiguous or undefined or confusing answer, you need to take a few steps back and approach the divide by zero issue from a
slightly different point of view.
Sure, if you try to divide say 10 by 0, the answer you get is hard to describe.
So, instead, lets approach this in a slightly different way.
Instead of dividing by 0, lets instead divide by 10 ... and of course the answer is 10/10 = 1. So far so good.
Now, lets use a slightly smaller number say 5 ... we now get an answer of 10/5 = 2.
Continuing in this fashion, let's now divide by 3 ... and we get 10/3 = 3.3333 (recurring).
Do you see whats happening here ? We're picking numbers that are getting closer and closer to zero and our answers are steadily getting bigger ... so
far we've used 10, then 5 and now 3. And our answers are 1, 2 and 3.3333
Lets now get even closer to zero without actually using zero itself, and see what happens to our answers.
Next we'll try dividing by 2 ... and we get 10/2 = 5.
Next we'll try dividing by 1 ... and we get 10/1 = 10.
Next we'll try dividing by 0.5 ... and we get 20.
Lets go even smaller and divide by 0.05 ... and we get 10/0.05 = 200.
Now try 0.0000005 .... and we get 10 / 0.0000005 = 20,000,000
And finally we'll use a very small number thats even closer to zero, say 0.000000000000000000005 which gives an answer of 20,000,000,000,000,000 ....
pretty darn big, huh !!!
So whats the lesson to be learned here ?
As can be seen from the examples above, dividing by zero is a special case that doesn't by itself give us any idea of what the answer is ... assuming
there's an answer at all.
But as we can see, by using a big enough starting number to divide by, then gradually making it smaller and smaller and smaller and trying to get as
close to zero as possible, we see that the answer we get simply gets bigger and bigger and bigger. So the closer we get to zero, the bigger our answer
So dividing by zero isn't so mysterious at all ... it's simply a mathematical case where the answer we get grows bigger and bigger as we get closer
and closer to zero itself ... without actually hitting zero.
In mathematical lingo, the answer tends to infinity as we approach a limit of zero.
edit on 29/8/11 by tauristercus because: (no reason