- #1
Andrax
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Homework Statement
we have this function
f(x)=1 if [itex]\frac{1}{x}[/itex][itex]\in[/itex] Z ( aka integer)
f(x) = 0 otherwise
Prove that limit (as x approach 0) dosen't exist (use the definition of limit - trying to prove that limit as x approchaes 0 and x approchs 0+ will not work here)<-- hint given by the exercise
Homework Equations
The Attempt at a Solution
so what I've done here , first of all this is obviously done by contradiction but just please correctr my mistaker here
let x=1/p /p is an integer (aka 1/x is an integer) then f(x) = 1
we have limit (as x approaches 0 ) 1 = 1
now let x=/ 1/p /p s an integer then
f(x)=0
then limit as ( x approaches 0 ) 0 = 0
we haven limit as ( x approaches 0 ) 0 and 1 which is impossible then it's a contradition please correct me here i know my proof is wrong but i couldn't correct it