Prove if lim(x sub n)=x and x>0 then there exists a natural number M such that x sub n > 0 for all n> or equal to M
Any hints on how to start this or what the end result should be would be greatly appreciated, thanks.
You can choose anything you like for , that is the definition of convergence for a sequence.
What we do is choose a particular value to ensure that is positive from onwards. We do this by choosing any value of then as for all we have:
so:
rearranging:
for all
But , so:
for all
CB