[過去ﾛｸﾞ] 現代数学の系譜 カントル 超限集合論他 3 (548ﾚｽ)
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54(2): 2020/07/28(火)11:04 ID:U9fCF8yb(1/6) AAS
>>42
補足

下記PDFで
”This new system would be constructed in a manner similar to Cauchy’s construction of the real numbers”
”Let us consider the factor ring
R~^N = R^N/ 〜Fr
where 〜Fr is the equivalence relation defined by
省28

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55(1): 2020/07/28(火)11:05 ID:U9fCF8yb(2/6) AAS
>>54
つづき

This is no different to saying that (an) is equivalent to (bn) if and only if
an = bn for all sufficiently large n. Thus the elements in our new system are
equivalence classes of real sequences, denoted by <an>. We now define the
relevant operations and order of our new system.

P14
省5

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56: 2020/07/28(火)11:09 ID:U9fCF8yb(3/6) AAS
>>54

ところで、このPDF
外部ﾘﾝｸ[pdf]:arxiv.org
Filters and Ultrafilters in Real Analysis 2012
Max Garcia Mathematics Department California Polytechnic State University

に、フレシェ・フィルター Fr を使って
”where 〜Fr is the equivalence relation defined by
省10

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