An algebraic brickwall (real analysis)

In summary, the conversation is discussing a goal to show yn=x, where n is an integer and x and y are real numbers. The proof involves finding an h value that satisfies certain conditions, and the conversation also mentions the need for further clarification on the problem statement.
  • #1
mynameisfunk
125
0
Goal: to show yn=x

This particular part of the proof supposes that yn>x. So we want
an h>0 such that (y-h)n>x

yn-(y-h)n<yn-x

yn-(y-h)n=(y-(y-h))(yn-1+yn-2(y-h)+...+(y-h)n-1)<hnyn-1

this yields h=(yn-x)/(nyn-1)


my question: how the heck does one derive h from this?
 
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  • #2
You are missing part of the problem statement. What are x and y?
 
  • #3
n is an integer, x and y are reals.

Sorry bout that.
 
  • #4
Seems to me you are still missing some of the problem statement. Maybe it needs to be of the form for all or for some something and something there exists something such that yn = x ?

With the somethings being integer and reals in some combination.
I think some for arrangements of somethings and the all/some the statement will be false, for others it will be trivial, maybe there is a nontrivial true case?
 

1. What is an algebraic brickwall in real analysis?

An algebraic brickwall in real analysis is a concept used to describe a situation where a function is continuous, but not differentiable at a certain point. This means that the function has a "brickwall-like" shape, where it is smooth on either side of the point but has a sharp corner or edge at that point.

2. How is an algebraic brickwall different from a regular brickwall?

An algebraic brickwall is different from a regular brickwall because it is a mathematical concept used to describe functions, while a regular brickwall is a physical structure. The term "brickwall" is used in both cases to describe a sharp change or discontinuity.

3. What are some examples of functions that exhibit an algebraic brickwall?

Some common examples of functions that exhibit an algebraic brickwall include the absolute value function, the square root function, and the inverse tangent function. These functions have a sharp corner or edge at a certain point, making them continuous but not differentiable at that point.

4. How is an algebraic brickwall related to the concept of differentiability?

An algebraic brickwall is related to the concept of differentiability because a function that exhibits an algebraic brickwall is not differentiable at the point where the brickwall occurs. This means that the function does not have a well-defined derivative at that point.

5. What are the implications of an algebraic brickwall in real analysis?

An algebraic brickwall has important implications in real analysis because it shows that a function may be continuous but not differentiable at a certain point. This means that the function may exhibit unexpected behavior or have a discontinuity at that point, which can have implications for its applications in various fields of mathematics and science.

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