[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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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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57(7): 2020/07/28(火)13:39 ID:U9fCF8yb(4/6) AAS
>>55
”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.”

１．Fr フレシェ・フィルター 使って、
　”to saying that (an) is equivalent to (bn) if and only if an = bn for all sufficiently large n. ”
　つまりは、十分大きなｎの先で一致する数列、(an) と (bn) との同値（equivalent）が定義できる
２．で？ Fr フレシェ・フィルター って、(an) と (bn) とか、具体的な数列には無関係なんですよね
　（>>50 "On the set N of natural numbers, the set of infinite intervals B = { (n,∞) : n ∈ N} is a Frechet filter base," とか PDF P8の”2.1.1 Definition (Fr´echet Filter). ”の通り）
省11

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