- #1
torquerotates
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So the definition states.( For any epsilon>0, there exists a delta>0 such that 0<|x-a|<delta => |f(x)-L|<epsilon. ) is equivalent to lim f(x)=L for x->a.
Well say f<=C some constant.
(reads less than or equal to)
then L<=C But that means that the epslion neighborhood can't extend past C. f is always going to be in (L-epsilon, L+epsilon). If L+epsilon>C, then there exists x* such that f(x*)>C. This puts a restriction on the values of epsilon. But the definition states that for ANY epsilon>0. epsilon should be as great as I want it. But it isn't.
Well say f<=C some constant.
(reads less than or equal to)
then L<=C But that means that the epslion neighborhood can't extend past C. f is always going to be in (L-epsilon, L+epsilon). If L+epsilon>C, then there exists x* such that f(x*)>C. This puts a restriction on the values of epsilon. But the definition states that for ANY epsilon>0. epsilon should be as great as I want it. But it isn't.