# Thread: Definition of limit as x approaches infinity

1. ## Definition of limit as x approaches infinity

Hi everyone!

I am not quite understanding the definition of a limit L as x approaches infinity. The definition states the following:

" We say that f(x) has the limit L as x approaches infinity and write

lim x->∞ f(x) = L

if for every number Є > 0 there exists a corresponding number M such that for all x

x > M -> |f(x) - L| < Є "

That is the definition from the book, and I don't understand what they mean by the number M. Can anyone explain what the number M is?

Thanks!

2. ## Re: Definition of limit as x approaches infinity

Originally Posted by Nora314
Hi everyone!

I am not quite understanding the definition of a limit L as x approaches infinity. The definition states the following:

" We say that f(x) has the limit L as x approaches infinity and write

lim x->∞ f(x) = L

if for every number Є > 0 there exists a corresponding number M such that for all x

x > M -> |f(x) - L| < Є "

That is the definition from the book, and I don't understand what they mean by the number M. Can anyone explain what the number M is?

Thanks!
M is an arbitarily large number that depends on epsilon.

Just like delta was an arbitarily small number that depends of epsilon.

So they are basically saying if we pick M big enough that for any x bigger than M f(x) is getting close to the limit (read less then epsilon)