I took a numerical analysis class in college where the professor focused on infinitismals. They were presented as the precursors to calculus. doing calculations with infinitismals is such a huge pain compared to calculus, I can see why people try to fit everything into the calculus bandwagon - it's a lot less work and cleaner!
Calculus is based upon the so-far correct premise that the
limit of a function as something goes asymptotic (your infinitesimal goes to zero) is the exact answer. Lynds seems to be waving away the premise that you can do that, and his solutions seem to be of the form, "There is no solution."
I forsee controversy.