What is the Definition of a Limit for a Function Approaching Negative Infinity?

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Homework Statement



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


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
 
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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"
 
Good.Thanks.
 
A more "standard" definition of
\lim_{x\rightarrow-\infty}f(x)=L
would be:

"Given \epsilon&gt; 0, there exist N such that if x< N, then |f(x)-L|&lt;\epsilon."

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