- #1
mikeyBoy83
So the definition of a bounded sequence is this:
A sequence ##(x_{n})## of real numbers is bounded if there exists a real number ##M>0## such that ##|x_{n}|\le M## for each ##n##
My question is pretty simple. How does one choose the M, based on the sequence in order to arrive at the conclusion? This has been something I've been confused about for a number of years and it seems like it all depends on the sequence in question. But is there a general rule that applies in these cases?
A sequence ##(x_{n})## of real numbers is bounded if there exists a real number ##M>0## such that ##|x_{n}|\le M## for each ##n##
My question is pretty simple. How does one choose the M, based on the sequence in order to arrive at the conclusion? This has been something I've been confused about for a number of years and it seems like it all depends on the sequence in question. But is there a general rule that applies in these cases?