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## Main Question or Discussion Point

I'm taking an introductory class on analysis right now and I'm trying to get through the book that we are reading. I'm having difficulty understanding a park of it and was hoping someone could help me out. The part I'm reading about now is on null sequences:

Here's an excerpt. I'm having trouble entering in the math type so sorry for no symbols.

1. Every null sequence is a bounded sequence. For - choose epsilon=1 - we have the |Z_nu|<1 for nu > mu, and hence the |Z_nu| is less than or equal to K = max(1, |Z_0|, ... ,|Z_mu|).

2.Let {|Z_nu|} be a null sequence. Suppose that for a fixed K the terms of a sequence {Z'_nu} under investigation satisfy the condition that, for all nu after a certain stage mu',

|Z'_nu| is less than or equal to K|Z_nu|.

I have some trouble understanding what this means. Mu here is the stage beyond which |Z_nu| is less than epsilon. I dont really understand the part about K = max (etc) or the Z', mu' part towards the end.

Thanks.

Here's an excerpt. I'm having trouble entering in the math type so sorry for no symbols.

1. Every null sequence is a bounded sequence. For - choose epsilon=1 - we have the |Z_nu|<1 for nu > mu, and hence the |Z_nu| is less than or equal to K = max(1, |Z_0|, ... ,|Z_mu|).

2.Let {|Z_nu|} be a null sequence. Suppose that for a fixed K the terms of a sequence {Z'_nu} under investigation satisfy the condition that, for all nu after a certain stage mu',

|Z'_nu| is less than or equal to K|Z_nu|.

I have some trouble understanding what this means. Mu here is the stage beyond which |Z_nu| is less than epsilon. I dont really understand the part about K = max (etc) or the Z', mu' part towards the end.

Thanks.