Thread: Uniform convergence

Is a horizontal line uniformly convergent??

Thanks.

Originally Posted by Benmath

Is a horizontal line uniformly convergent??

Thanks.

as in for all and converging uniformly to (where is a constant)?

you tell me, does this satisfy the definition of what it means to be uniformly convergent?

I would say yes it is uniformly convergent. I have a line x=2.

So f_n(x)=2 and f(x)=2. Their difference is 0 implying uniform convergence.

Originally Posted by Benmath

I would say yes it is uniformly convergent. I have a line x=2.

So f_n(x)=2 and f(x)=2. Their difference is 0 implying uniform convergence.

x = 2 is a vertical line. so unless you are interpreting it like or something, it won't make sense. but yeah, a difference of zero everywhere implies uniform convergence

Oops that was dumb, I meant the line y=2. Sorry. Thank you!