dkv: ?I agree. But I do not agree that limit to 0 is same as zero.?
No, it is not. But in your case, the evaluation of your function in zero is NOT DEFINED, it DOES NOT EXIST, axiomatically speaking.
dkv: ?Zero exists in reality and classically at least, there is nothing called tends to zero. We can achieve perfect 0. Maths uses the concept of infinitesimal for its convenience to divide the undividable.?
Once again, since when does math describe the physical reality? And no, math uses the concept of limit to define also functions like the tangent to a curve, to calculate areas and volumes, and so on and so forth.
dkv: ?IT has rules to do so...and gives accurate results...My argument is that the process must map to the reality, the INPUT, the PROCESS and the OUTPUT must map to the reality at every point?
In within limits. As I said, and I am stressing this again, mathematics is only a tool, and as such it is applied within certain ranges of validity. What matters is only the meaning of the mathematical symbols, and physics assumes its right to use math as it sees fit, and within limits that are not mathematical in nature.
dkv: ? This statement has a very DEEP MEANING. Limit should not only be consistent with Maths but also with the reality. (Please understand I am not against any of the existing concepts of Maths or Physics but I wish to enrich it if possible.).?
It has a meaning only to you, and maybe the Pythagoreic school, but not to any physicist. The concept of infinitesimal is very clear in classical physics, the concept of a limit is also very clear in physics, but no one makes the claim that the mathematical description should be consistent with reality in all the cases. That?s why there is something called classical physics, using one sort of math, quantum physics, using a different math, and so on and so forth.
You cannot enrich mathematics in relation with nature, because while the former is abstract, our knowledge of the latter is empirical, obeyng rules that are not mathematical in essence.
dkv: Agree this was not a suitable example but my desire was to share the concept with simplicity. Can a function be understood at all points and becomes non-understood at certain points or at exact 0(or any other exact no.)?
For the last time now, your function is NOT DEFINED at x=0. As such, it does not exist at that point and mathematical logic tells you that you cannot have any type of knowledge, complete or incomplete, about something that does not exist.
dkv: ?After transformation the position of my so called collapse has changed but it was not removed from the system. If theory intends to remove it completely then with its current capabilities we can say that it will fail to do so...(after enough digging one will rediscover its new position)?
Well, you used the wrong tool. The wrong representation for your function. As I said before, if you take the arctg of your function, you singularity disappears.
dkv: ?Give me some time I will find out a real classical case of collapse.?
Be my guest.
dkv: I also need to revisit this thought..
Once again, be my guest.
dkv: What if it does not meet to reality in with its full force...Why is it that it allows certain intermediate steps in the derivation to exist independent of reality when it is describing it. How do you explain complex numbers used extensively in Physics.
It does not meet reality in full force, as you say it. But this is no problem. Physics only uses what considers necessary and how it considers it necessary. Physics is not dictated by the math, even though math is a very useful tool to ?speak? physics.
In this view, complex numbers are just a convenient way to describe certain issues in physics.
dkv: ?Yes Sir , I understand that 0 is not origin, but yes I would like to call it a reference point and there is no need to associate it with existence and non-existence.?
It is not a reference point either. You cannot allow yourself to be biased in your views either as a mathematician or as a physicist.
Boolean algebra is more than enough to handle such concepts. We are more interested in classifying the reality relative to a reference. That the reference point could ever be absolute or not is a separate question. Correct me if I am still wrong.
I am sorry to say this, but you are wrong. We don?t need to classify reality with respect to a reference, although may think the opposite. The definition of reality itself, even in philosophical terms, transcedes the necessity of a reference.
dkv: ?I am afraid that the singularity can never be removed. Because there logically it can not be removed from Maths. Unless it accepts that INPUT,PROCESS and OUTPUT of a derivation must map to the Reality.?
In your case, of course it can be removed. See above how. And it does not need to map to reality, but to a (very) small fraction of reality, namely the one that can be described by it.
