- #1

MathematicalPhysicist

Gold Member

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im having trouble with this simple question, here's what i did:

|x-1/2|<d implies |f(x)-1/2|<e. f(x) assumes only rational values so

( I am guessing that by 'assumes' it's input is rational values, so

|x-x0|<d |f(x)-f(x0)|<e f(x0)=p/q

if p/q>1/2 then |f(x)-p/q|<|f(x)-1/2|<=e

and if p/q<1/2 |f(x)-1/2|<|f(x)-p/q|<e, and thus the limit of f(x) at x0 always converges to 1/2.

is this right?