Nothing Factor
There are many curious things about division.
One of the many mysteries is 0.
We all know that a/0=undefined.
But what if it was 0/0??
Or 0^0?
There are 3 possible answers for zero divided by zero.
Using the Properties of 0, Properties of Recipricals, Properties of Division,
Find all 3 possiblities of 0/0.
One of the many mysteries is 0.
We all know that a/0=undefined.
But what if it was 0/0??
Or 0^0?
There are 3 possible answers for zero divided by zero.
Using the Properties of 0, Properties of Recipricals, Properties of Division,
Find all 3 possiblities of 0/0.
posted by James Yu at
7:43 PM
7 Comments:
0/0 could be 0
0/0 could be +infinity
0/0 could be -infinity
0/0 could be undefined
0/0 could be NAN (not a number)
It depends on the setting or maybe the type of application. Generally it is said to be undefined so computation stop to prevent errors that will follow in a series of computations. But it may be possible to use limits to perdict where the outcome might be if it were possible. Without this I would say 0/0 is probably nothing of value.
0^0 is one; there is no room for ambiguity in that proof. Anything raised to the zero-th is one, regardless of whether the base is zero. This is because 2^2 = 1*2*2, we always start with 1 as our starting point. 0^2 = 1*0*0, thus 0^0=1.
The three "possibilities" that you are referring to are as follow:
a/a = 1; set a=0, 0/0 = 1
a/0 = infinity (not true, common misconception), set a=0, 0/0 = inf.
0/a = 0, set a=0, 0/0 = 0.
Please note: you can not divide by zero. Hopefully this is the last time this comes up for some time on this site. It's not a rule, it's a law. Division means just that, dividing something-- "We have 4 apples, we have 2 people, we want to give equal shares to each person 4/2 = 2. Now, replace "2" with "0" . "We have four things and we want to divide them evenly amongst zero people" It is impossible to do this. It defies physics, because it involves the destruction of matter. If you smashed the apple into a "seemingly infinite" number of pieces, so small that they were invisible to the human eye, it would "seem" as though you had destroyed matter, when in fact you clearly did not. You simply divided the apples amongst a very small number of people, close to zero, like .00000000..001
In less theatrical terms, to debunk the "infinity" theory, as the denominator of a fraction approaches zero the quotient approaches infinity.
I thought of another
0/0 =1
because something divided by the same should be 1.
Ah, yes, if it were a law, you should be able to prove it. But in truth, if you are dealing with limits, then 0^0 is an indeterminate form, but if you are dealing with ordinary algebra, then 0^0 = 1.
Daniel is right, what a stupid question.
Ragknot, you're an idiot.
I agree with previous "anonymous".
Can we now dispense with puzles relating to zero.
Sometimes the only correct answer is not to play the game.
Post a Comment
Links to this post:
Create a Link
<< Home