You are saying that limits and calculus are completely broken and cannot be used. You’re saying we have to throw away calculus and replace it with — nothing!

But there are two problems with this.

First, people didn’t just make up the theorems of calculus — they proved them using formal mathematical proofs. If you’re going to say that calculus is wrong then you need to explain why these proofs are wrong. You can’t just wave your hands and use vague philosophical arguments — you need to actual refute the mathematical proofs.

You would first need to demonstrate that you understand these proofs, and then explain why these proofs are false. You haven’t shown you understand any of them, and, I hate to say it, my most likely hypothesis is that you haven’t even read them and tried to understand them.

Mathematics is a complex, formal game played with extremely specific rules and symbols, rules and symbols that have been carefully worked out over hundreds of years by some of the greatest minds humanity has ever produced. You’re free to invent your symbols, or make up your own rules, but you have to formalize your arguments. You can’t just come in and say, “I have no idea how this works but it’s wrong because [lots of words].” You have to do mathematics to play.

The second problem is completely practical — it’s that calculus works.

Look around you — at the buildings, airplanes, computer chips, all of this technology that has evolved over centuries. All of this technology has always relied on the correctness of calculus and it works. Even our most basic concepts like “force” and “power” are defined using calculus.

You are saying, “This is all wrong.”

I say, “The electronics that very internet upon which we communicate are built on depend on calculus in every of their construction.”

Worse, you aren’t even giving us an alternative tool to you! You’re like, “It’s all wrong, but I don’t have an alternative.” Who’s going to buy that?

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Let’s go through your sentences one at a time and hopefully find the issue

In the real world, in physics, the first statement is true — the Uncertainty Principle guarantees it. However, the second sentence is false. There is nothing inconsistent between dimensionless points in spacetime, and motion and change, and you don’t explain why this would be so.

The third sentence restates the the first and is true. The fourth statement restates the second and is false.

The last statement is key: “Indeed, defined as it is, as a succession of instants, time itself couldn’t exist.”

Here’s the root of the problem! Time is not a succession of instants.

In mathematics, time is a continuous real-valued variable — and this is not a succession of points in time, even though you can perfectly well talk about points in time. A continuous real number has order without succession.

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So what are continuous real-valued variables then? The full answer is fascinating, even beautiful — to say in English that the real numbers are an uncountable continuum doesn’t convey its grandeur at all.

To get you to that point would take a considerable amount of work — far more than I have time for here. You should take a calculus course! You’d probably have a lot of fun if you didn’t fight with the teacher.

I feel you are missing out on the true amazingness of what mathematicians far too drily call “analysis” by your insistence that it doesn’t exist.

That you have a — I hate to say it — false model of what calculus is doesn’t mean you aren’t intelligent — it means you are incredibly stubborn.

Every math student goes through the same phase you do at some point when they learn analysis. Some drop out. But if you persist, you will finally understand that Zeno’s brilliant “paradoxes” actually represent deep truths about countable vs uncountable and continuity.