No they don't, for example quantum tunneling, which is a fundamental term of advanced integrated electronics, does not obey your hypothetical notion of Limits (barriers), and it is developed exactly because quantum phenomenon exists simultaneously at both sides of your deductive-only hypothetical notion of Limit (barrier). .
You are mixing mathematical concepts with observed phenomena. Physical limits are quite different than abstract limits. For example, the mechanics and biology of your body imposes limits on your performance. Suppose that you can't swim faster than 2 MPH. But that doesn't mean that you can't swim faster and go over the limit without making adjustments to your body. Simply switch from swimming in the pond to the river-swimming -- direction downstream. That's the simplest concept of quantum tunneling.
One way involving the Heisenberg uncertainty principle is central to our conceptual understanding of Quantum Mechanics. It defines a theoretical limit on how precisely we can know both the position and the momentum or the energy and time of a particle. This idea is often used to explain the phenomena of tunnelling. The uncertainty principle predicts that for a small amount of time the particle might 'borrow' energy from the system so that it can 'jump' over a mountain. That is, since there is a limit on how precisely we can theoretically know the particle's energy, it might have a higher energy than we would expect it to, allowing it to cross the barrier.
When you are swimming downstream, your body is borrowing energy from gravity propelled mass of water.
There are limits that are not that easy to overcome. The Neanderthals came to existence, moved to the caves, and after some 200,000 years, they were still in there.
Imagine this problem to solve: There is a step pyramid. How many step does it take to get on the top of the pyramid?
The limit that prevents to uniquely solve the problem is that there is not enough data to deduct the solution. But the formulation of the problem never mentions any unique solution -- the stereotype acquired in schools does. So when you break the limiting stereotype, you can either use arbitrary solution or non-arbitrary one. The latter is far more desirable.
There are many non-arbitrary solutions. One strategy is based on switching from hypothetical to imaginary/real. Just imagine that there is a real step pyramid. So you go up and count the steps. Now when you reach the top, you need to go back to tell the guy who asked you about the height of the pyramid your finding. So there is this double movement up and down and there are also two points where you no longer climb or descend. It follows that the shortest pyramid is 2 steps tall and looks like this:
121
The higher pyramid looks like this:
12321
And the higher pyramid looks like this:
1234321
Is there any limit to the progression?
The limit must be some change, like
GO is to COMPOSITE as STOP is to PRIME:
121 = composite
12321 = composite
1234321 = composite
123454321 = composite
12345654321 = composite
1234567654321 = composite
123456787654321 = composite
12345678987654321 = composite
12345678910987654321 = prime
And so if you chose a non-arbitrary solution and say that the pyramid is 10 steps tall, then it is up to the demon who gave you the puzzle to figure out the non-arbitrary means of solution.
Which option is correct?
1) GOD doesn't exist.
2) G0D doesn't exist.
1) GOD doesn't exist.
2) G0D doesn't exist.
That would please your English teacher, but vould make His Omniscience climb the walls in well-rehearsed dispair.