I wouldn’t go so far as to say nonsense, but dysfunctional. In a “real world application” where the universe in finite, we cannot have “infinite distance from its origin”. However, we can say as time approaches infinity, then distance will approach infinity. Schooner didn’t specify, so I’m assuming Object B has constant velocity, so it kinda misses the point about applied forces.
But he agrees that when we say “0.999… = 1”, we mean they are the exact same number. That means 0.000… = 0, and life is worth living again.
sigh It is a math problem. Not a science experiment bro !! sheeeesh
Use mathematics (where the infinity concept exists) to figure out what the angle AC is at infinity. Not an actual experiment to see how small you can get the angle, lololol
You are asking a series of though questions. I think you are working with general
relativity and quantum physics, perhaps even with their unification.
I don’t know exactly what makes you say that if 0.999… ≠ 1, that means that 0.000… ≠ 0. At first I thought that since every number is equal to itself then
if 0.999… ≠ 1, therefore 0.000… = 0.
So how to make sense of what you are saying, I began to wonder.
If 0 is not equal to itself, what is it, can it be anything, can 0 = ∞ ?
What is 0.00000…? Is it limit? The limit of 0 ?
Maybe 0 and infinity can be limits of each others, so that they are situated
at an infinitesimal distance from each others.
Are you talking about the principle of least action when you write that “If I apply a force over the instantaneous time interval and evaluate it’s effect on an object”?
Next you are talking about vector spaces. I think they are relevant when dealing with
general relativity and quantum physics. In general relativity a mathematical coordinate system becomes physical space, the form of space-time. Perhaps
real numbers represent vectors if the coordinate system is physical. Can you locate
a point where 0 = ∞ if co-ordinates represent a physical space?
Next you wonder if complex numbers form a vector space. I think that complex numbers are not vectors, they behave differently than vectors under multiplication.
We do have a concept called a complex vector, that is a vector with complex numbers
as coefficients, but this concept is different than complex number.
Your next question deals with torque, it is defined as cross product of two vectors
at right angles to each others. But I don’t know if this is what you are expecting
as an answer.
If Object B is in motion, then time is very much involved. Please attend to my answer to 7…7 as there I will attempt to clarify my inadequately stated query.
The logic I’m using is: If 0.999… ≠ 1, then 1 - 0.999… ≠ 0, then 0.000… ≠ 0. If this holds to be true, then we have real mischief in what’s observed in the Classical universe (which is the universe where Newton’s Laws of Motion and Gravity hold true in all places at all times).
Simply, a vector space is the complete set of all vectors. This set has the property that adding any two vectors yields yet another vector, and multiplying any vector by a complex number also yields another vector. Turns out, complex numbers themselves share these exact two properties. From this it can be proved (although I personally can’t) that there exists between vectors and complex numbers a one-to-one correspondence. For each and every complex number, there is one and only one vector. This also holds true over the addition operation, the sum of two complex numbers and the sum of the corresponding vectors are themselves corresponding.
Ergo, every statement made about real numbers must also be true for vectors. What I’d like for you to do is for every proof you offer for real numbers (which also apply to complex numbers), please state the proof for vectors. This is all addition, so everything must be the same for both vector spaces.
I’m pretty sure vectors can have complex number magnitudes.
Thank you … that didn’t even cross my mind … phaw … math is a young person’s sport.
Whoosh, vector magnitudes must be an element of the complex numbers … so no infinity. Time cannot be both zero and approaching infinity. Frankly, if you want to ignore time here, that’s fine … but as pointed out above, the statement of a limit must include a reference. We cannot sat “the limit of A is B”, we have to say "the limit of A as C approaches D is B.