Hilbert problem 15 required understanding Schubert's book. In this book, reducing to degenerate cases was one of the main methods for enumeration. We found that nonstandard analysis is a suitable tool for making rigorous of Schubert's proofs of some results, which used degeneration method, but are obviously not rigorous. In this paper, we give a rigorous proof for Example 4 in Schubert's book, Chapter 1. §4 according to his idea. This shows that Schubert's intuitive idea is correct, but to make it rigorous a lot of work should be done.
Banghe LI
. HILBERT PROBLEM 15 AND NONSTANDARD ANALYSIS (I)[J]. Acta mathematica scientia, Series B, 2020
, 40(1)
: 1
-15
.
DOI: 10.1007/s10473-020-0101-4
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