Careful, thorough, and following strict rules—the opposite of loose or casual reasoning.
Robinson's non-standard analysis(as a mathematical development)
Abraham Robinson's mid-20th-century mathematical framework that made infinitesimals rigorous and respectable by showing they could work in a formal logical system, not just as intuitive ideas.
Vindicates(as used in philosophy of science)
Proves that something was right or justified, usually by showing evidence that supports it after there was doubt.
infinitesimal(Nonstandard analysis)
A hyperreal a whose absolute value |a| is less than 1/(n+1) for every natural number n
Δx (delta x)(as mathematical notation)
A symbol meaning 'a small change in x'—in this case, a tiny change in some quantity; Δx² means that tiny change squared.