0
Wrong answer above. A limit is not the same thing as a limit point. A limit of a sequence is a limit point but not vice versa. Every bounded sequence does have at least one limit point. This is one of the versions of the Bolzano-Weierstrass theorem for sequences. The sequence {(-1)^n} actually has two limit points, -1 and 1, but no limit.
Wiki User
∙ 8y ago
Wiki User
∙ 7y agoA sequence, {xn}, is said to converge to a limit x if, given any e > 0, however small, there exists an integer k, such that abs(xk - x) < e for all n >=k. That is all value of the sequence, from xk onwrads, are no further from x than e.abs(xk - x) < e => -e < xk - x and x - xk < e which implies that xk is bounded.
Wiki User
∙ 13y agoIt cannot be proven because it is not true.
The sequence t(n) = (-1)n is bounded: by -1 and 1 but it does not have a limit point: it oscillates.
Nai'Lah Miller
The best answer is no answer
Add your answer:
Earn +20 pts
How was the Andes mountain range formed?
The Andes Mountains were formed through subduction of the oceanic plate underneath the South American plate.
What is the start of a film called?
American IdolAnswera tv show that starts with a in Amanda show Answera tv show that starts with a in Amanda show AnswerAmerican Dad, Alias
What is the difference between title sequence and opening credits?
The title sequence of a film is the opening scene(s) that include dialogue and often action, whereas the opening credits show the cast and crew in writing, often accompanied by a song and/or some acting in the background.
Who is the woman in the opening sequence of The Game TV Show?
Actually, it's Shanti Lowry. Wendy Raquell Robinson said so today on Wendy Williams Show. http://www.imdb.com/name/nm1283650/?ref_=nv_sr_1
What caused the Andes mountains to form?
They were formed by deposition and by convergent boundaries
Examples of bounded and not convergent sequence?
(0,1,0,1,...)
Every uniformly convergent sequence of bounded function is uniformly bounded?
The answer is yes is and only if da limit of the sequence is a bounded function.The suficiency derives directly from the definition of the uniform convergence. The necesity follows from making n tend to infinity in |fn(x)|
How do you prove that the sum of a convergent sequence divided by n will converge?
You can use the comparison test. Since the convergent sequence divided by n is less that the convergent sequence, it must converge.
What is Example of bounded sequence which is not Cauchy sequence?
((-1)^n)
A convergent sequence has a LUB or a what?
JUB
Is every cauchy sequence is convergent?
Every convergent sequence is Cauchy. Every Cauchy sequence in Rk is convergent, but this is not true in general, for example within S= {x:x€R, x>0} the Cauchy sequence (1/n) has no limit in s since 0 is not a member of S.
Any convergent sequence is a Cauchy sequence is converse true?
no converse is not true
What is a sequence which is not convergent defined as?
It could be divergent eg 1+1+1+1+... Or, it could be oscillating eg 1-1+1-1+ ... So there is no definition for a sequence that is not convergent except non-convergent.
Are the major lithospheric plates bounded by diverging and converging boundaries?
They are divided by divergent, convergent AND transform boundaries.
Is the limit exists for a monotone sequence An?
If a monotone sequence An is convergent, then a limit exists for it. On the other hand, if the sequence is divergent, then a limit does not exist.
Every convergent sequence is bounded is the converse is true?
For the statement "convergence implies boundedness," the converse statement would be "boundedness implies convergence."So, we are asking if "boundedness implies convergence" is a true statement.Pf//By way of contradiction, "boundedness implies convergence" is false.Let the sequence (Xn) be defined asXn = 1 if n is even andXn = 0 if n is odd.So, (Xn) = {X1,X2,X3,X4,X5,X6...} = {0,1,0,1,0,1,...}Note that this is a divergent sequence.Also note that for all n, -1 < Xn < 2Therefore, the sequence (Xn) is bounded above by 2 and below by -1.As we can see, we have a bounded function that is divergent. Therefore, by way of contradiction, we have proven the converse false.Q.E.D.
What is convergent sequence?
A convergent sequence is an infinite sequence whose terms move ever closer to a finite limit. For any specified allowable margin of error (the absolute difference between each term and the finite limit) a term can be found, after which all succeeding terms in the sequence remain within that margin of error.
