How to write this in terms of epsilon and deltas?

Thread starter InbredDummy
Start date Jul 29, 2007
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Epsilon Terms

In summary, epsilon and delta are mathematical variables used in the definition of limits in calculus. They represent a small, positive number and a small interval around a given value, respectively. They are used in writing mathematical expressions to precisely define and prove the existence of limits. Limits are written in terms of epsilon and delta by stating that for every positive number epsilon, there exists a positive number delta such that if x is within a distance delta of L, then f(x) is within a distance epsilon of L. Choosing appropriate values for epsilon and delta is crucial in accurately defining and proving the existence of limits, as they need to hold for all possible values of x close to the specified value L. An example of writing a limit in terms of epsilon and

Jul 29, 2007

InbredDummy

How do I write that given a set S, every epsilon neighborhood of infinity (in the complex plane) contains at least one point of S?

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Jul 29, 2007

Kummer

I do not understand the question?
What is S? And what does it mean "epsilon neighborghood of infinite".

And you statement is clearly wrong given that S is empty.

Related to How to write this in terms of epsilon and deltas?

What is the definition of epsilon and delta in mathematical terms?

Epsilon and delta are mathematical variables used in the definition of limits in calculus. Epsilon (ε) represents a small, positive number and delta (δ) represents a small interval around a given value.

Why do we use epsilon and delta in writing mathematical expressions?

Epsilon and delta are used in writing mathematical expressions to represent the concept of a limit, which is the value that a function approaches as its input approaches a certain value. Using epsilon and delta allows us to precisely define and prove the existence of limits.

How do you write a limit in terms of epsilon and delta?

A limit is written in terms of epsilon and delta as follows: given a function f(x) and a limit L, we say that "the limit of f(x) as x approaches L is equal to L" if, for every positive number ε, there exists a positive number δ such that if x is within a distance δ of L, then f(x) is within a distance ε of L.

What is the significance of choosing an appropriate value for epsilon and delta?

Choosing appropriate values for epsilon and delta is crucial in accurately defining and proving the existence of limits. The values of epsilon and delta need to be chosen carefully to ensure that the limit statement holds for all possible values of x close to the specified value L.

Can you give an example of writing a limit in terms of epsilon and delta?

As an example, the limit of the function f(x) = x^2 as x approaches 2 can be written as: "for every positive number ε, there exists a positive number δ such that if x is within a distance δ of 2, then f(x) is within a distance ε of 4."