# Definition of a Limit.

1. ### azatkgz

196
1. The problem statement, all variables and given/known data

Given a function $$f:R\rightarrow R$$ and a number L,write down a definition of the statement

$$\lim_{x\rightarrow-\infty}f(x)=L$$

3. The attempt at a solution

Is it just $$\lim_{x\rightarrow-\infty}f(x)=\lim_{x\rightarrow\infty}f(-x)$$ ?

and definition is
for $$\forall \epsilon>0$$ $$\exists N$$ such that $$\forall n>N$$
we have $$|f(-x)-L|<\epsilon$$

2. ### quasar987

4,773
assuming by n you mean x, then yes, this looks like a good dfn, although the usual dfn is that "for all e>0, there is an N<0 such that x<N ==>|f(x)-L|<e"

196
Good.Thanks.

4. ### HallsofIvy

41,260
Staff Emeritus
A more "standard" definition of
$$\lim_{x\rightarrow-\infty}f(x)=L$$
would be:

"Given $\epsilon> 0$, there exist N such that if x< N, then $|f(x)-L|<\epsilon$."

Notice that in neither this definition nor your definition is N required to be an integer.