If R->R satisfies f(x+y)=f(x)+f(y) for all x,y in R and 0 is in C(f), then f is continuous. show me a great proof... thanks in advance
Follow Math Help Forum on Facebook and Google+
Originally Posted by antoniowilliams46 If R->R satisfies f(x+y)=f(x)+f(y) for all x,y in R and 0 is in C(f), then f is continuous. show me a great proof... thanks in advance A great one huh? This is obvious since and thus . Thus, now there exists some such that . Make
thats all that i need???? nothing more???
Originally Posted by antoniowilliams46 thats all that i need???? nothing more??? You need to say more but that is the entire idea.
still need help on what to say in the proof
i still need a proof for this one
Do you understand Drexel proof? If you tell me where you get lost, I may be able to help you.
I dont know where to go after abs val of x-y is less than delta.
Let z=x-y. Then . Another way to see it is: f is continuous at x iff f(x+h)=f(x)+o(1) as . So in this case, f(x+h) = f(x) + f(h) by linearity and f(h)=o(1) by continuity at 0.
View Tag Cloud