definition

In definition of topology, why we say intersection of finite members of τ belongs to τ. What is harm in any number of members of τ in it?

I must prove that the derivative of x^2/3 is 2/3x^-1/3 by using the definition but I don't know where to go after the initial plug in , that is if I even did it right. lim ((x+h)^2/3-(x)^2/3)/h h->0

Hello, I'm new to the forum and I'm taking a linear algebra class with a very hard professor. My question is this. From the course textbook (Jean Gallier 2013, Basics of Algebra, Topology, and Differential Calculus) it says; "The set R of real numbers has two operations + : RXR-->R...

Hi guys, im stuck at this problem, trying to prove that limx->0 (cos 1/x2) has no limit. Its obvious that cos (1/x^2) = cos (1/0^2) = cos (0) is undefined, but how to show it using the formal definition of limit ? where im at: 0 < X-0 < delta cos (1/x^2) - L < epsilon hints please ? :-)

The following is an excerpt from Milne's Group Theory lecture notes handed down on Winter 1994 at the University of Michigan. Could somebody please explain me the highlighted passage in the document? It's very small.

The question here is what is the derivative of 3^x... okay its ln(3)3^x... i need to show this not by using the derivative rules but using the limit definition and i have no idea how to start.

If someone were to ask you to define what a limit is as presented in a first semester calculus course without using technical language, what would your definition be?

Hi i am currently working on questions where i am required to determine the least upper bound a set if there is one to do this i have been given the following strategy Given a subset E of R to show that M is the least upper bound, or supremum, of E, check that: 1.x\leq M for all x \in E 2...

Find the limit of (x^2 + 3x) as x tends to -3. Then use the epsilon-delta definition to prove that the limit is L. I enjoy limit questions but when it comes to the Epsilon-Delta Definition material, I never get it.

I am reading Ernst Kunz book, "Introduction to Plane Algebraic Curves" I need help with some aspects of Kunz' Definition 1.1. The relevant text from Kunz' book is as follows: In the above text, Kunz writes the following: " ... ... If K_0 \subset K is a subring and \Gamma = \mathscr{V}...

In your own words, what makes a person a mathematician? Do you consider yourself a mathematician? Why? Why not?

f(x) = x^2-5x b) Find f''(x) second derivative?

In the movie Stand and Deliver, the actor playing famous high school math teacher Jamie Escalanted is quoted as saying that the Mayans defined zero as the "absence of value." Is this true? Is zero the ABSENCE OF VALUE? What is your definition of zero?

Attached file is the sample in TEX file, provided by AIP for conference proceeding: I have error when I tried to run \begin{definition} *** \end{definition} \begin{theorem} *** \end{theorem} etc. What can I do?

Does this work as a direct proof? If the cross product is associative, then (A x B) x C = A x (B x C). Consider when A = B. One the left side we have: (A x A) x C = 0 x C = 0·C·sinθ·n(AxA)xC= 0, where θ is the angle between vector A and C and n(AxA)xC is the unit vector perpendicular to...

Part of the definition of a function is to specify its domain. How about an equation like, x^2+2x = -1, is it "proper" to refer to the "domain of an equation" ? If not how would one specify the set from which it draws its solution set? Thanks.

My answer is wrong. Can anyone spot my mistake?

These questions are really tedious. I've checked my work 3 times already and I don't see any mistakes. I know it's wrong because the computer rejects my answer (my answer is boxed). Please refer to the image.

For the given lim as x approaches a of f(x) = L and Epsilon, use the graph of the function f to find the largest value of Delta such that if 0 < |x - a| < Delta, then |f(x) - L| < Epsilon. (i) lim as x approaches 16 of √x = 4; Epsilon = 0.1

Can anyone spot my mistake? The correct answer is highlighted in green, and my answer is highlighted in yellow. My answer is sort of identical to the right answer.