Abstract
The main contribution of the paper is the critique of J.M. Henle’s Non-nonstandard analysis [The Mathematical Intelligencer 21 (1) (1999) 67]. The principal criticism of Henle’s work is the failure to do away with the axiom of choice as he claims he would. Therefore, it suffers from the same flaw that Robinson’s Nonstandard Analysis has [Nonstandard Analysis, North-Holland, Amsterdam, 1966]. However, the paper also summarizes the new mathematics and physics generated by the resolution of Fermat’s last theorem [Nonlinear Studies 5 (2) (1998) 227] and the solution of the gravitational n-body problem [Nonlinear Analysis 30 (8) (1997) 5021], respectively, including the resolution of the problems, paradoxes, contradictions and unanswered questions of mathematics and physics except the Bieberbach’s conjecture and the Riemann hypothesis. Highlighted in the paper are astonishing results coming from the new real line (i.e., the reconstructed real line) as well as the proof of Goldbach’s conjecture and the natural ordering of the new real line (which does not exist in the real line).
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