Definition:Order Type of Rational Numbers/Historical Note
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Historical Note on Order Type of Rational Numbers
The use of $\eta$ to denote the order type of $\struct {\Q, \le}$ dates back to the writings of Georg Cantor and Felix Hausdorff.
According to Winfried Just and Martin Weese in their Discovering Modern Set Theory. I: The Basics of $1996$, this order type, along with that for $\struct {\R, \le}$, has not been greatly studied in recent years.
$\eta$ is in fact far more often used to denote a general ordinal.
Sources
- 1996: Winfried Just and Martin Weese: Discovering Modern Set Theory. I: The Basics ... (previous) ... (next): Part $1$: Not Entirely Naive Set Theory: Chapter $2$: Partial Order Relations: Mathographical Remarks