Sometime, I believe perhaps 2 years, ago I asked a question about breakthroughs, such as those within mathematics and physics which may lead a whole discipline forwards in many ways. One example from physics (perhaps also mathematics) is Newton’s Principia.
I considered the problem of infinitesimals, used by Newton and criticized by idealist bishop Berkeley as “ghosts of departed quantities”, being “neither finite of infinitely small” (by which I assume he meant =0). We consider this contradiction to be solved by the modern concept of the mathematical limit, by a relation between e.g. epsilon and delta.
My question was the following:
If this breakthrough (which I attribute to Cauchy) was a significant step forward, why did we not see a number of significant advances as a consequence such as for Newton and Leibniz regarding celeste mechanics?
I now take the view that the question was never properly answered. It was also put on hold being considered unclear. I also believe that I now have a clear answer: the concept can be used to define the real numbers. I am not sure but I guess that this was the first of several methods of defining the set of real numbers. That amounts to a major consequence, does it not?