Actually, limits and infinitesimals are two very different explanations/foundations for calculus. Infinitesimals are much more intuitive. Up to last decade, li

Actually, limits and infinitesimals are two very different explanations/foundations for calculus. Infinitesimals are much more intuitive. Up to last decade, limits were the only rigorous enough explanation. Until someone invented an equally rigorous reconstruction of calculus with infinitesimals.