Prove that all convergent sequences are bounded

  • #1
was looking at a proof of this here: http://gyazo.com/8e35dc1a651cec5948db1ab14df491f8

I have two questions,

why do you set K = max of all the terms of the sequence plus the 1 + |A| term? Why do you need the absolute value of all the terms? i.e. why |a_1| instead of |a_1|?
 

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  • #2
LCKurtz
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was looking at a proof of this here: http://gyazo.com/8e35dc1a651cec5948db1ab14df491f8

I have two questions,

why do you set K = max of all the terms of the sequence plus the 1 + |A| term? Why do you need the absolute value of all the terms? i.e. why |a_1| instead of |a_1|?

Because ##|x_n|< L+1## only holds for ##n > N##. If some of the first ##N## terms are larger than all the rest, use the biggest one of them for the bound.
 

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