Editing 2735: Coordinate Plane Closure
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{{w|Coordinate planes}} are used in math for drawing graphs. The joke here is that a small section has been "closed for maintenance," likening the concept of a coordinate plane to an actual physical platform used by math, which is therefore vulnerable to damage such as is shown in the comic. In reality, the coordinate plane cannot be damaged as it is not a tangible thing.{{citation needed}} | {{w|Coordinate planes}} are used in math for drawing graphs. The joke here is that a small section has been "closed for maintenance," likening the concept of a coordinate plane to an actual physical platform used by math, which is therefore vulnerable to damage such as is shown in the comic. In reality, the coordinate plane cannot be damaged as it is not a tangible thing.{{citation needed}} | ||
β | Closure in mathematics can be a term relating to sets, specifically operations on sets, and a coordinate plane is a particular set of numbers. A set is closed under an operation if all the "answers" to the operation are also in the set. The coordinate plane is said to be closed under vector addition for example - adding together any two coordinates produces another coordinate in the plane. Many functions and operators may be said to have closure on the real plane, and this comic may be a pun on that term. However, if there actually is a hole in the plane, then suddenly the plane will no longer exhibit closure. | + | Closure in mathematics can be a term relating to sets, specifically operations on sets, and a coordinate plane is a particular set of numbers. A set is closed under an operation if all the "answers" to the operation are also in the set. The coordinate plane is said to be closed under vector addition for example - adding together any two coordinates produces another coordinate in the plane. Many functions and operators may be said to have closure on the real plane, and this comic may be a pun on that term. However, if there actually is a hole in the plane, then suddenly the plane will no longer exhibit closure. More on closure can be found here: {{w|https://en.wikipedia.org/wiki/Closure_problem}} |
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Closure can also be used in another sense, relating to the topology of a set; roughly speaking, a description of what parts of the set are "close" to others. In this sense, if one takes the closure of a plane with a hole, the result is indeed an intact plane, provided the hole is sufficiently (infinitesimally) small. | Closure can also be used in another sense, relating to the topology of a set; roughly speaking, a description of what parts of the set are "close" to others. In this sense, if one takes the closure of a plane with a hole, the result is indeed an intact plane, provided the hole is sufficiently (infinitesimally) small. | ||