現代数学の系譜工学物理雑談古典ガロア理論も読む62

[過去ﾛｸﾞ] 現代数学の系譜工学物理雑談古典ガロア理論も読む62 (1002ﾚｽ)
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206: 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE  [sage] 2019/03/13(水) 07:24:46.64 ID:QlfKIGCF

>>205

つづき

P94
CHAPTER III THE WELL-FOUNDED SETS
§ 1. Introduction
Some questions about sets are irrelevant to mathematics.
First irrelevant question. Is there anything which is not a set? Certainly
there is in the "real world" of cows and pigs, but our axioms of set theory
say nothing about this "real world", since we have declared that they talk
only about sets - in fact, hereditary sets (see I §4). Furthermore, the Axiom
of Extensionality has embodied in it the assertion that all things in our
domain of discourse are sets. It seems likely that we have not left any interesting
mathematics behind by so restricting our universe, since mathematical
objects like R and C are hereditary sets and have been defined
explicitly within this domain in I § 11.
(引用終り)

つまり、ZFCでは、現実世界の素朴集合論の「 "real world" of cows and pigs」は、対象外だと
(部分引用)
”Is there anything which is not a set? Certainly
there is in the "real world" of cows and pigs, but our axioms of set theory
say nothing about this "real world", since we have declared that they talk
only about sets - in fact, hereditary sets (see I §4). ”
(引用終り)
以上

http://rio2016.5ch.net/test/read.cgi/math/1551963737/206

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