A mathematics teacher on LinkedIn asked the following.
Is Nothing by Nothing One?
I posted the following as comment #195.
Ramanujan's teacher said that if there were three students and he had three bananas to be distributed, then each student would get a banana. Perhaps the teacher was trying to drive home that "n divided by n is equal to one: n / n = 1". Ramanujan had a doubt and asked the teacher, "Sir, if no banana is distributed to no student, then will each student get one banana?" It is not known as to what the reaction of the teacher was. This anecdote can be interpreted, with hindsight, to reveal Ramanujan's inquisitive, intuitive nature, to realise that there could be exceptions to the division rule. Or, he might have liked the teacher to state more precisely, n / n = 1, for all n, except for n = 0". Ramanujan told his friends, that the answer to the question of what is the value of 0 / 0 may be anything. The zero of the numerator may be many times the zero of the denominator and vice versa. The value cannot be determined. SOURCE http://bit.ly/1TSyMqE
I am no genius, and in my mid-fifties, my insights have only come through a lot of reading and thinking.
So I posted the following as comment #204. I didn't want people to think I agreed with Ramanujan on this question.
1] Addition and multiplication and growth, are synthesis or composition of quantity, whether concrete or abstract.
2] Subtraction and division and decay, are analysis or dissolution of quantity, whether concrete or abstract.
1] must precede 2]. From the synthesis of multiplication, we arrive at a product. This product generated, ONLY THEN may be subjected to the analysis of division.
That is why all mathematical andragogies, that today are pedagogies, sequence the understanding of quantitative relationships as follows.
Sort (i.e. put apples with apples and bananas with bananas, or sort fruit)
Count (form a correspondence relation. i.e. 1 apple per person)
Add (how many apples do we have?)
Multiply (how many apples are needed for a no. of people for a no. of days?)
It is not possible to analyse ideas of quantity that have not been composed.
Thus 0/0 has no meaning. It is not anything, as Ramanujan joked.