👉 In mathematics, an ultrafilter is a type of filter that captures all sets in its domain. An ultrafilter on a set A is defined as a collection of subsets of A that are closed under finite intersection and complementation (i.e., for any two non-empty intersections of elements from the collection, their complements are also in the collection). An ultrafilter on a set A can be thought of as an ideal that captures all sets that are "too small" to be included in A.
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What is the definition of Ultrafilterability? 🙋
👉 Ultrafilterability, also known as ultrafilter completeness, is a mathematical property that refers to the ability of an infinite set of non-empty sets (or sub-sets) to be well-ordered by inclusion. This means that there exists a well-ordering $<$ such that every two elements in the set are comparable under this order. In other words, if we have a finite set $A$ and an infinite set $B$, then it is possible to find a maximal element of $B
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What is the definition of Ultrafilter? 🙋
👉 In mathematics, an ultrafilter on a set X is a subset of X that satisfies the following properties: 1. The union of all elements in the filter equals X. 2. If x is any element not in the filter, then x must be in the filter. For example, consider the set {x ∈ R | x < 3} and the ultrafilter generated by this set (the set of all numbers less than 3). The union of all elements in this filter equals R
What is the definition of Ultrafilter? 🙋
👉 ULTRAFILTER: (sneezes) Oh no! My superfiltered filter's broken again. It was a pain to try and breathe through.
EXCUSES MINE: "Umm... Yes?" ULTRAFILTER (screams in terror): I just made this ridiculous joke, it's going to be my funeral!" EXCUSES ME: "What's the problem? You're making fun of me." THE SENSE OF UNPLUGGED: "UGH! Ugh! What are you guys laughing at? I'm being so rude!" ULTRAFILTER (whips out a large knife): This is what happens when you don't take your superfiltered filter seriously. It's like, literally cutting through anything it touches. EXCUSES ME: "How dare you?" THE SENSE OF UNPLUGGED: "UGH! Ugh! What are you guys laughing at? I'm being so rude!" ULTRAFILTER (tears up in frustration): This is what happens when someone breaks your filter. They make you feel like a complete nobody. EXCUSES ME: "What the hell does that mean?" THE SENSE OF UNPLUGGED: "UGH! Ugh! What are you guys laughing at? I'm being so rude!" ULTRAFILTER (whips out a large knife): This is what happens when someone breaks your filter. They make you feel like a complete nobody. EXCUSES ME: "What the hell does
