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$$(\forall \epsilon>0)(\exists \delta>0)\rightarrow \left| f(x) - c \right|<\epsilon$$
well that proved it if you're going to zero, my bad
I don't think so
you don't think so what? That proves it for any finite x. The infinite proof is slightly different
constant is constant always it will not change anymore regarding a change of anything
change in climate doesnot change the position of a tree. it is constant.
so limit of a constant is constant always not zero
noufal i don't think you understand delta-epsilon proofs, with the wording of your response. And the limit of a constant is zero if the constant is zero.
The limit of a constant as x approaches infinity is that constant. This can be shown using delta-epsilon.
which is what i proved above for finite x.
The infinite proof is:
\[(\forall \epsilon>0)(\exists N>0)(\forall x>N)(\left| f(x)-L \right|<\epsilon)\]
f(x) = C and L = C, so
\[\left| f(x)-L \right|=\left| C-C \right|=0<\epsilon\]
so any x>N may be chosen to satisfy the proof.