Why why why (tiny limsup proof)

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In summary, "Why why why (tiny limsup proof)" is a mathematical concept that involves proving the existence of a limit superior in a sequence of numbers by repeatedly asking "why" until reaching the desired result. The term "tiny" refers to breaking down a complex problem into smaller, simpler steps, while "limsup" is the maximum value that a sequence can approach. This concept is used in mathematics to break down complex problems and understand underlying principles, but it may not always be the most efficient method and may not work for all types of sequences.
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quasar987
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There's a "theorem" in my book that says if x is a cluster point of {x_n}, then lim inf(x_n)[itex]\leq[/itex]x[itex]\leq[/itex]lim sup(x_n).

The way the author proves it is a little bit extravagant. Why not just say "Let A be the set of all cluster points. Then, lim inf(x_n)=inf(A)[itex]\leq[/itex]x[itex]\leq[/itex]sup(A)=lim sup(x_n)."

?
 
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Don't they pretty much say the same thing?
 

What is the concept of "why why why (tiny limsup proof)"?

"Why why why (tiny limsup proof)" is a mathematical concept that involves proving the existence of a limit superior in a sequence of numbers by repeatedly asking "why" until reaching the desired result.

Why is it called "tiny limsup proof"?

The term "tiny" refers to the fact that the proof involves breaking down a complex problem into smaller, simpler steps. "Limsup" is short for "limit superior," which is the maximum value that a sequence of numbers can approach as the number of terms in the sequence increases.

What is the purpose of using "why why why" in this proof?

The use of "why" in this proof is a way to break down a complex problem into smaller, more manageable steps. By repeatedly asking "why," we can trace the steps back to the initial conditions and prove the existence of the limit superior.

How is "why why why (tiny limsup proof)" used in mathematics?

"Why why why (tiny limsup proof)" is used in mathematics to prove the existence of a limit superior in a sequence of numbers. It is a useful tool for breaking down complex problems and understanding the underlying principles behind mathematical concepts.

Are there any limitations to using "why why why (tiny limsup proof)"?

While "why why why (tiny limsup proof)" can be a helpful tool in proving the existence of a limit superior, it may not always be the most efficient method. In some cases, there may be more direct or straightforward ways to prove the same result. Additionally, this method may not work for all types of sequences, so it is important to consider alternative approaches as well.

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