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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
(an)〜Fr(bn) if and only if {n : an = bn} ∈ Fr.
This is no different to saying that (an) is equivalent to (bn) if and only if
an = bn for all sufficiently large n. ”
省25

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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
Chapter 3
Non-standard Analysis
3.1 Construction of the Hyperreals *R
省2

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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
(an)〜Fr(bn) if and only if {n : an = bn} ∈ Fr.”
数列のシッポの同値ってやってますよね

で？
省7

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