Strange question?

Question

if n/n is 1, n/0 is infinity, 0/n is 0, what is actually 0/0? 1? 0? or infinity?

Answer 1

It is undefined.

Think about it: 10:5 means the number you have to multiply by 5 in order to get 10. Following this definition, n:0 (where n is not 0) would mean the number you have to multiply by 0 in order to get n. However, anything multiplied by 0 is 0, so n:0 does not make sense.

It's another thing that if the numerator of a quotient goes to n (where n is positive) and the denominator goes to 0 (and is positive) then the quotient goes to plus infinity (in terms of limits). Infinity is not a real number, and n/0 is left undefined by convention. Also note that if the numerator goes to n (positive) and the denominator goes to 0 but it is negative then the quotient goes to minus infinity.

Similarly, 0:0 would mean the number you have to multiply by 0 in order to get 0. However, any number multiplied by 0 is 0, so 0:0 could be any number, violating the convention that addition, subtraction, multiplication and division should give a unique result.

Of course, it could be defined as anything (as 0 for example), like the square root operation gives two answers and for the sake of a unique answer, we define sqrt(a) to be the positive square root of a.

However, if the numerator and the denominator of a quotient both go to 0 then the quotient can go to anything including 0, 1, +infinity, -infinity and any real number, or it may not even exist.

Examples:
a) 0/0=0: limit of (1/n^2)/(1/n) = limit of 1/n = 0.
b) 0/0=1: limit of (1/n)/(1/n) = limit of 1 = 1.
c) 0/0=a: limit of (a/n)/(1/n) = limit of a = a.
d) 0/0=plus inf.: limit of (1/n)/(1/n^2) = limit of n = +infinity.
e) 0/0=minus inf.: limit of (-1/n)/(1/n^2) = limit of -n = -infinity.
f) 0/0 is undefined: limit of (1/n)/[1/n*(-1)^n] = limit of (-1)^n does not exist.

For this reason, defining 0/0 to be something (e.g. 0) would violate the rule that if c goes to A and d goes to B and A/B is defined then c/d goes to A/B, so it would be a rather useless definition.

Answer 2

Any division by 0 is undefined, When 'n' is divided by a number APPROACHING 0,(Not zero) like 0.000000000.....(A '1' ends the decimal), then the value is infinity. So 0/0 is totally undefined.

Answer 3

Anything/0 is not defined (so it's not infinity), at least not in any area of mathematics I've ever encountered. Well, I didn't really say much with that, a first-year university maths module I'm taking now is the highest level I can rely on ;)

Answer 4

0/0 is an UNDEFINED form. x/x as x goes to 0 has a LIMIT of 1.
There is a subtle but important difference.

Answer 5

0/0 could take any value depending upon the functions you put in numerator and denominator. because of this reason the term 0/0 is dubbed indterminate.

Answer 6

0/0 is the same thing as n/0, since n can be any number.

Answer 7

The concept of nothing is infinite.
Therefore if you divide infinity by infinity you end up with the square route of infinity. This is infinity, as infinity times infinity will still equal infinity as nothing can be greater than infinity.

Answer 8

0/0 is undefined. you can't divide any number by zero

Answer 9

All of the above, but only at limits.

Answer 10

n/0 is not infinity, it doesn't exist. See my answere at http://answers.yahoo.com/question/index?qid=20061024104941AA29rFc&r=w&pa=FZptHWf.BGRX3OFMhzVSUZ3flUm7xCkulXX6fa2AsmQGKL61ovebFhaBYixQ3wG.15j1z6ZhUA0SgvceVw--#RcIpDjftUGMurmU.oZIBDgTQP9NO40uJBSOgrJNMdNyMhO5lQjpa