"...only one laughing..."

You are illustrating the reason that mathematicians generally disparage the concept of an "infinitesimal", when it's used as proof rather than conceptual aid. (Yes, I know about https://en.wikipedia.org/wiki/Non-standard_analysis)

Not only do you get wrong conclusions, you get tedious, hard-to-adjudicate arguments.

I agree with your thought, and that of the majority of mathematicians for many years, that infinitesimals are better construed heuristically than literally.

You mention that you know of non-standard analysis and indicate that it's irrelevant. Though I don't know why you think this, I agree with you. I just wanted to plug non-standard analysis as both mathematically interesting and also very useful. One can jettison the philosophical thought that NSA "vindicates" the historical use of infinitesimals (as I think we should), while still seeing NSA as the wonderful and deep piece of math that it in fact is.

Thanks for your support, but I never said anything about non-standard analysis. I made one post in support of its parent, and people jumped on it to say how wrong I am, as apparently I accidentally stumbled over a sore spot in mathematics. I don't know why infinitesimals apparently aren't allowed, but the tone around here has convinced me to not care.

And now every post I have made in this thread tree is getting downvoted. So I'm out. Y'all can argue about nothing--and nearly-nothing--by yourselves.

What would that be?

If c>0 were smallest, then c/2 would be smaller and still positive!