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.

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- Oct 10th 2008, 11:54 PMhayter221Another limit proof
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. - Oct 11th 2008, 12:01 AMCaptainBlack
- Oct 11th 2008, 12:08 AMhayter221
I'm not sure I follow, what do I do with the epsilon...sorry I have just begun to learn this and I haven't fully grasped the idea of the limit definition.

- Oct 11th 2008, 05:45 AMCaptainBlack
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 - Oct 11th 2008, 11:38 AMhayter221
thanks, much appreciated!