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f : ]-1,1[ to R
f(0)>0
Prove that if f is continuous on 0 then ∃ a in ]0,1[,
for all x in ]-a,a[ f(x)>0
It seems evident but i don't know how to prove it.
f is continuous on 0 <=> f(x) ---> f(0)>0
>>
assume f is cont but there is no such a
that makes f(x)>0 on (-a,a) forall x
no matter how small our a is ?!
so f(0) <= 0 due to continuity around 0
choose c in (-a,a) st f(c)<= 0, f(c) goes to f(0) as a goes to 0. why? cont'y of f . So f(0)<=0
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>>311732
>]-1,1[
>][
FUCKING KILL YOURSELF
>>
>>311747
Thanks.
>>
>>311754
>>][
>boundaries not included in the interval
?
>>
>>311808
it's () faggot
>>
>>312039
its the same, mr knowitall
https://en.wikipedia.org/wiki/ISO_31-11#Sets
>>
>>312089
>Inventing new notation for no reason
Kill yourself and the faggots at ISO
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