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.
Ahh… someone with at least a tiny bit of education…
That could be true except to refer to hyperreal numbers requires that one use hyperreal notation or at very least specify such. A variety of hyperreal notations have been offered by pretty well known mathematicians. I have my own notation (for philosophical reasons). And another thing that is required, although unknown to many mathematicians, is logic. Mathematics is a subset of logic and cannot defy logic in its construction without becoming incoherent and useless.
Again, if using proper notation, “0” is undefined because the “degree of 0” isn’t being specified.
0.000…:000 / 2 would still be 0.000…:000
or my own notation:
[0.000…:0R] / 2 = [0.000…:0R] {R == “eternally Remaining amount for sake of non-ending decimals”}.
That is an excellent observation, although I would disagree with your logic.
One cannot divide 2 by a null set, because the statement itself makes no sense (hence is “undefined”). But dividing nothing yields nothing, always. The number of parts requested is irrelevant. Thus;
0/2 = 0, just as standard analysis proposes.