Definition of limit as x approaches infinity
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?
Re: Definition of limit as x approaches infinity
M is an arbitarily large number that depends on epsilon.
Originally Posted by Nora314
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)