Recent content by cesc

Could you give a concrete example where X is an element of X

well the example seems kind of frivolous. Also, I'm not sure if its quite right. The word "list" has the dual meaning of a set, and a piece of paper which is an expenseAre there any examples involving mathematical objects?

How come you have a reading course for a first course in algebra? wouldn't you normally have just as part of coursework?

I understand how the argument goes- let X be the set of all sets which don't contain themselves. If X contains itself, then X is not in X If X doesn't contain itself, then X is X the part i don't understand is, What on Earth does it mean for a set to contain itself? garbage in, garbage...

ah, thanks for the counterexample.it would only be continuous at 0. My second post was to clarify a technical point. If f is undefined at every point except a, and defined at a, is f continuous at a?

check that The vector space of set of the polynomials is isomorphic to the space X a0+a1+a2=...an-1=0 now find a basis for X

Homework Statement f is a function that satisfies f(x+y)=f(x)+f(y) and f is continuous at 0. prove f is continuous everywhere Homework Equations The Attempt at a Solution its easy to see that f(0)=0 My hunch is that the only soln f= cx, and f=0; but otherwise can't make...

it boils down to the definition of the limit. for all e>0. there exists s>0 such that if x satisfies abs(x-a) then abs(f(x)-a)<e the question is: Does f have to be defined on the interval abs(x-a)? example of this- A function is undefined at every point except a. does the limit...

Homework Statement Suppose a function is continuous at a point, c. Does this mean there exists an interval around c which is also continuous? If so prove Homework Equations The Attempt at a Solution