Book:Keith Devlin/The Joy of Sets: Fundamentals of Contemporary Set Theory/Second Edition/Errata

Errata for 1993: Keith Devlin: The Joy of Sets: Fundamentals of Contemporary Set Theory (2nd ed.)

$\S 1$: Naive Set Theory:

$\S 1.7$: Well-Orderings and Ordinals:

Theorem $1.7.11$

Also, since:

$\ds X_x$

$=$

$\ds \set {z \in X \mid z \le x}$

$\ds $

$=$

$\ds \set {z \in X \mid z \le y \land z \le x}$

$\ds $

$=$

$\ds \set {z \in X_y \mid z \le x}$

$\ds $

$=$

$\ds \paren {X_y}_x,$

we have

$(2): \quad \paren {g_y X_x}: X_x \cong \paren {\map Z y}_{\map {g_y} x}$.

Now, $\map Z y$ is an ordinal, so by Theorem $1.7.6$, $\paren {\map Z y}_{\map {g_y} x}$ is an ordinal.

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