It is obvious you’re not overly familiar with mathematics, but I can’t help but notice how despite writing “since infinitesimals don’t exist” several times in your post, you fail to give any kind of proof for this assumption. I hope you don’t consider such a ludicrous line as “few advocate actual infinitesimals because an actually existing infinitesimal is indistinguishable from zero” your proof.
You also fail to define “existence”, and the post you link to does little else than go to great lengths to avoid this issue. There’s a difference between 2∈ℕ, 2∈ℝ, 2∈ℂ and so on; and a meaningful question isn’t whether 2∈ℕ “exists” but whether ℕ is a good enough approximation of some parts of reality. Likewise, your question whether infinitesimals exist should be rephrased as whether ℚ (or ℝ or anything similar) is a good enough approximation of some parts of reality. Assuming the hypothesis of quantization this is not the case for anything made of mass/energy, but I see no reason why the same should be said of anything that is not, like time or space.
It is obvious you’re not overly familiar with mathematics, but I can’t help but notice how despite writing “since infinitesimals don’t exist” several times in your post, you fail to give any kind of proof for this assumption. I hope you don’t consider such a ludicrous line as “few advocate actual infinitesimals because an actually existing infinitesimal is indistinguishable from zero” your proof.
You also fail to define “existence”, and the post you link to does little else than go to great lengths to avoid this issue. There’s a difference between 2∈ℕ, 2∈ℝ, 2∈ℂ and so on; and a meaningful question isn’t whether 2∈ℕ “exists” but whether ℕ is a good enough approximation of some parts of reality. Likewise, your question whether infinitesimals exist should be rephrased as whether ℚ (or ℝ or anything similar) is a good enough approximation of some parts of reality. Assuming the hypothesis of quantization this is not the case for anything made of mass/energy, but I see no reason why the same should be said of anything that is not, like time or space.
Your argument is, at best, incomplete.