X divided by Y means X number of elements equally distributed across Y number of groups. The result of division is not the number of elements that remain in the original, undivided, pool of elements but the number of elements in each one of the divisions.
31 divided by 0 means 31 elements equally distributed across 0 number of groups. How many elements do we get in every group after such an operation? But there are no groups – there are 0 groups – so we can’t really answer. Therefore, the result is undefined.
Ecmandu is speaking of a different operation – not division – and he does so because he thinks that words precede concepts rather than the other way around.
Division is not a subtractive operation. You do not remove elements from the starting pool of elements using certain method then count how many elements remain. That’s not division.
Similarly, multiplication is not an additive operation.
If our language implies it, then that’s the problem of language, and you shouldn’t confuse it for a mathematical problem.
There are no existents, no states, in multiplication and division. You are speaking of different operations – ones you made up, invented, imagined, created in your head.
Because the result of division is the number of elements within each one of the groups. We are counting the number of elements within groups, not the number of elements outside of these groups. When there are no groups, there is nothing to count, therefore, the result is undefined.
Ecmandu this is getting silly. Now everyone is telling you that you are wrong but you are not listening to them. You have to realise
that maths is useless unless there is universal agreement on the function of its axioms and everyone here know this apart from you
The concept of existence Becomesrelevant issue here.
The consciessness which makes meaning manifest in
this context, brings the patent theory of meaning to the fore, thereby ‘existence’ gains meaning.
Which brings to the fore the the idea of 0 as symbolic of nothingness. A nothingness which has a double value: a conceptual nothingness, and a functional nothingness.
How does this relate to consciousness of the void qua nothingness, as a lack of existence?
The significance of this train of thought lies in another difference, but one which subsumed the former, vis: conscience as a self differentiating function, or as a pre-existing field of possibility.
In the later case, the field or whatever you designate it, ‘exists’ prior, not in the temporal sense, of course,
but in the sense of a a shift away from a quantifiable difference.
This difference is evident in the sharp difference in the awareness of human beings away from animals.
The quanta(fiability) has changed the quality of awareness to a high degree and has progressed to the awareness of the in-it’s self, as a probable field.
In this sense, the idea of 0 , as nothingness, has gained a material substance.
You can divide by this, but it is always self consuming, and always results with the same result, = 1. It is the most basic logical equation, the law of identity.
I hate to agree with you for the appearance of a necessary presumption, but if you don’t get side-railed, then there is no danger of a misinterpretation.
I’m not a mathematician so bear with my inexperience… but I don’t think that anybody here has actually stipulated which definition of “0” they are working with?
If 0 is understood as a Robinson infinitesimal in non-standard analysis, then 2/0 does indeed equal infinity, and 0/2 does indeed equal 0 (I think. I’m not pretending I understand non-standard analysis - I read about it in a book). On the other hand, if 0 is considered as “the null set”, the expression 0/2 is simply not admissible because the null set does not contain 2 subsets. (In fact you might like to argue, just to be mischievous, that to be divisible by 2, the null set would have to contain three subsets - can you guess why?)
Mathematics is another language altogether, and what you expressed pretty well describes the philosophical underpinnings of the different meanings of 0. Mathematically, 0 deals with value in the abstract, whereas 0=nothingness deals with the
s
ubstantial, philosophical underpinnings of meaning.
So we are in essence speaking in similar subsumed equivalencies.