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!

Metric given by (d) in the textbook on page 48 in the following url. How could we plot this function and characterize what the metric looks like for varying a, b, c. Start by plotting the case when d(x,0)=1, a=b=c=1. Vary a, b, and c individually. Show plots for each case and Characterize how...

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?