0/0 is undefinened for a very simple reason. Say you are dividing 35/7. If you were in elementary school, you would be taught to, say take 35 objects and arrange them in 7 equal groups. Then, count how many are in each group, and, voila, there are 5. So 35/7=5. The same works for any fraction or mixed rational number (divide by the numerator, multiply by the denominator) and if the answer isn't whole, just take the number in each group and add it to the remainder over the original. This whole delicate framework falls apart when dividing by 0. Lets say you have two constants, x and y, where x+1=y. So, if dividing by 0 led to a result of 0, then:
x/0=y/0 and x+1=y
*0 *0
x=y and x+1=y
Substitution
x+1=x
This doesn't work. x can't be 1 less than x. Therefore, division by 0 is not allowed. But, then there is the case of 0^0. There is a long debate about what 0^0= (some say it equals 1, others, 0, others, undefined). So, depending on who you ask, you could hear A: "Zero, stupid.", B: "Actually, since zero to the power of zero is equal to one, zero divided by zero equals one.", C: "It's undefined, since no division by zero is allowed.", or what I would say, D: "It's complicated."
