Recent content by fabbi007

Any help is greatly appreciated!

Homework Statement d(x,y)=(a|x_1-y_1|^2+b|x_1-y_1||x_2-y_2|+c|x_2-y_2|^2)^{1/2} where a>0, b>0, c>0 and 4ac-b^2<0 Show whether d(x,y) exhibits Triangle inequality? Homework Equations (M4) d(x,y) \leq d(x,z)+d(z,y) (for all x,y and z in X) The Attempt at a Solution I...

How can you prove that if a mapping F:X->Y is both left and right invertible that there exists only one left inverse and one right inverse. I am trying to understand the theory, I could understand the example though. Can you give me a hint?

Thanks Mark. I get it now. It is indeed a square matrix and there is only one inverse. Also since from definitions if a mapping is both left and right invertible then it has an inverse, meaning only one inverse.

Thanks for the latex code Mark. This is from my electrical engineering course. Hence I posted here. Also, the above mapping is right invertible because from the definition the range=Y. Would there be different left inverse and right inverse for a mapping if it is both one-to-one and onto? My...

Homework Statement relation from R^2-->R^2 ( R is real line) (y1) [0 1] (x1) (y2) =[-1 1] (x2) is this left invertible? if so what is the left inverse? y1,y2 are element in a 2by 1 matrix, same with x1, x2. the elemenst 0,1,-1,1 are in a 2x2 matrix. I did no know how to...

They are equal!

R is real line, C is set of Complex numbers If we considered the Euclidean metric on RXR a. Show whether the Euclidean metric on R RXR is a metric. b. Show whether the Euclidean metric on C C is a metric. c. Generalize the Euclidean metric to a set made up of all n-tuples of real...

So no every function is subset of the Set N.

you are saying there is no one-to-one. The other person here is saying there is equality. Conflicting!??

So in this mapping the range of f(m) = N hence the mapping is onto and hence Card(N even)= Card (N). I think I got it now! Thanks for the huge explanation both of you.

I am lost here and confused by the ideas. What are the other mappings like n-->n/2? n-->2power n? I am tending to believe the cardinality is equal but hard to come to a conclusion . Please help.

This part I do not get. There is one-to-one and onto between them?

well for the given mapping n->n the range is subset of N, hence card(N even)< card (N). I am blindly going by the definition. I am missing anything here? Can you please elaborate on what your thoughts are CRG?

CRG: The definition from Nayler and sell says that card(X)<card (Y) if every one-to-one mapping phi of X into Y is not onto, that is, the range phi(X) is a proper subset of Y. Range of the mapping in the above problem is (2,4,6,8...) is a proper subset of N, right?