This scholar shows Irrationality -contradictions-is no hindrance to something being 'true'
"With all these paradoxes and inconsistencies Bunch notes that it is “… amazing that mathematics works so well.” Since the mathematical way of looking at the world generates contradictory results from that of science, such as the mathematical notion of the continuum, and quantum mechanical concept of quanta. As Bunch notes “… the discoveries of quantum theory or the special theory of relativity were all made through extensive use of mathematics that was built on the concept of the continuum…that mathematical way of looking at the world and the scientific way of looking at the world produced contradictory resultsB. Bunch, Mathematical Fallacies and Paradoxes, Dover, 1982, p.209-210
"“Newton and Leibniz developed the calculus…. Their ideas were attacked for being full of paradoxes.” Newton’s formulation of calculus was self-contradictory yet it worked. Newton worked with small increments going of to a zero limit. Berkeley showed that this leads to logical inconsistency. The main problem Bunch notes was “that a quantity was very close to zero, but not zero, during the first part of the operation then it became zero at the end.” B, Bunch , Mathematical Fallacies and Paradoxes Dover, 1982, p.192. These paradoxes where resolved by the time old expediency of mathematics by defining them away in the nineteenth century by Cauchy and Weierstrass. Up until then calculus was used pragmatically such that “instead of having demonstrations justify results, results were used to justify demonstrations.I. Gratten-Guinness, From the Calculus to set theory 1630-1910, Duckworth, 1980, p.296.
there is a whole book wriiten on Quantum paradoxes
F. Selleri, Quantum Paradoxes and Physical Reality, Kluer Academic Publishers, 1990,
quote-from other scientists
Now even though quantum mechanics is paradoxical no experiment has contradicted quantum theory predictions and quantum theory is the most successful that has ever existed in science.
"Similarly there is ample evidence of theories giving the predicted results even though they collapse into absurdity i.E. Are self-contradictory or paradoxical such as those in quantum mechanics- just as there is in mathematics. Heisenberg notes that “ the strangest experience of those years was that the paradoxes of quantum theory did not disappear during this process of clarification; on the contrary they have become even more marked and exciting.” F. Selleri, Quantum Paradoxes and Physical Reality, Kluer Academic Publishers, 1990, p.V111.
Wick state the orthodox view when he says “here my opinion of the orthodox quantum mechanics, ...The belief concealed is that Nature has been found in a contradiction. But quantum physicists are not simpletons. In their hearts they know such a claim is philosophically unacceptable and would be rejected in other sciences.”
Wick notes “ I believe orthodox quantum theorists [slates] reason, ... The microscopic world exhibits paradoxes or contradictions and this fact is reflected in the best theory describing it.” A. Wick, The Infamous Boundary, Birkhauser, Berlin, 1995, p.184
This question seems not to understand the concept of map-territory relations. Of course math and science lead at some point to paradoxes, they are imperfect maps of the universe we live in. As such, at their extreme edges they often work off of approximations that are accurate enough to be indistinguishable from correct results relative to perception at normal scales. Working with a number unimaginably close to a number when you should be simply working with that number will give you results unimaginably close to correct, though they are very slightly inaccurate.
This is why gravity is a good theory to describe the motion of planets but very poor at describing the motion of particles. Planets work with distances vast enough that the effects of the strong, weak, and electromagnetic forces are lost in the overpowering effects of gravity. Thus, if you just calculate what gravity predicts, you get very, very, very close to being perfectly accurate. If you're working with protons, however, the other three forces are much more important, and gravity becomes much more wildly incorrect by itself.
What may look like paradoxes in math and science are really just points at which our models of the universe break down. And it's a good thing that they do this. After all, the only way to have a perfect, completely accurate map is to make it exactly the size and shape of the territory it is mapping. We sacrifice accuracy so that we get a piece of data small and simple enough for us to process while still being a generally good guide around the territory. In order to have math and science that fit the universe perfectly, we'd have to make them as complicated as the universe is, and that would defeat the point of having them because they are essentially theoretical tools used to simplify and check what we see.
Saying "calculus sometimes uses zero and sometimes uses very very nearly zero," is like looking at a map and complaining that you can't see individual grass blades.