Abstract
In this chapter we present some useful odds and ends that should be a part of everyone’s mathematical tool kit, but which don’t conveniently fit anywhere else. Our presentation is informal and we do not prove many of our claims. We also use this chapter to standardize some terminology and notation. In particular, Section 1.7 introduces a number of kinds of binary relations.
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In an ideal world, we would never interchange the statements “A includes B” (meaning В ⊂ A) and “A contains B” (meaning В ∈ A), but the distinction is often harmlessly ignored.
Quoted in E. T. Bell [27, p. 477].
In case you have not heard it before, Russell’s Paradox goes like this. Let S be the set of all sets, and let A = {X ∈ S : X ∉ X} ∈ S. If A ∈ A, then A ∉ A. On the other hand, if A ∉ A, then A ∈ A. This paradox is avoided by denying that the class of all sets is itself a set.
Be aware that some authors use Ω to denote the first uncountable ordinal and w to denote the first infinite ordinal.
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© 1994 Springer-Verlag Berlin Heidelberg
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Aliprantis, C.D., Border, K.C. (1994). Odds and ends. In: Infinite Dimensional Analysis. Studies in Economic Theory, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03004-2_1
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DOI: https://doi.org/10.1007/978-3-662-03004-2_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-03006-6
Online ISBN: 978-3-662-03004-2
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