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chessbrah
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I'm thinking proof by contradiction but I can't seem to get anywhere.
I agree. I have moved the thread to "Homework and Coursework- Calculus and Beyond".PAllen said:May I ask why this thread is here? It isn't number theory, and it looks like homework to me.
Closure is a mathematical concept that refers to the smallest set that contains all the elements of a given set. It is often denoted by a bar over the set, such as A̅.
If A is a subset of B, it means that all the elements of A are also elements of B. A can be equal to B or it can be a proper subset, meaning that it contains some but not all of the elements of B.
If A is a subset of B, then the closure of A is also a subset of the closure of B. This is because the closure of A will contain all the elements of A, which are also elements of B, and therefore will also be contained in the closure of B.
The concept of closure is important in many areas of mathematics, including topology, functional analysis, and abstract algebra. It allows us to define limits, continuity, and completeness in a more general and abstract way, leading to deeper insights and applications.
An example of a set and its closure is a set of rational numbers and its closure, which is the set of real numbers. Another example is a set of open intervals on a real line and its closure, which is the set of closed intervals on the same real line.