What do the variables in the equation mean?

[Teachme]

I uploaded a picture of the definition for a limit of a series. I am wondering if anyone knows what the meaning for variables M and N are. Thanks for reading.

 

[epenguin]

It is just mathematical language and expression habits to get used to. N could otherwise be called (and often is) 'some integer' and M 'some number' which when that sequence → ∞ exist and have that property.

In words that phrase means 'that the sequence a_n tend to infinity means any number you can think of no matter how large will be less than all of the a_n when n gets bigger than some integer.

You may ask why don't they say that? Well the way they say it gives you a lead into what to actually do when you are given an example of a sequence and asked to show whether it dos or does not → ∞ .

 

[Teachme]

Thanks a lot, I really appreciate it. Your answer is very helpful. Thanks!