Category:Initial Segments
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This category contains results about Initial Segments.
Definitions specific to this category can be found in Definitions/Initial Segments.
Let $\struct {S, \preceq}$ be a well-ordered set.
Let $a \in S$.
The initial segment (of $S$) determined by $a$ is defined as:
- $S_a := \set {b \in S: b \preceq a \land b \ne a}$
which can also be rendered as:
- $S_a := \set {b \in S: b \prec a}$
That is, $S_a$ is the set of all elements of $S$ that strictly precede $a$.
That is, $S_a$ is the strict lower closure of $a$ (in $S$).
By extension, $S_a$ is described as an initial segment (of $S$).
Subcategories
This category has only the following subcategory.
Pages in category "Initial Segments"
The following 4 pages are in this category, out of 4 total.