Question

Anybody familiar with Real Analysis?

Answer 1

a bit, post your question

Answer 2

I need to give an example of a sequence, so that a sub sequence converges any given number L

Answer 3

I'm in real analysis right now. When I had to do a problem like that, the idea was to use more than one variable. So for example:
\(a_{n}\ = \frac{1}{n} + L\) with \(L,n \in\ \mathbb{N}\)
The idea is that n can go to infinity and will simply converge to L. Im not knowledgable enough about it to go all fancy proof-like with it, but that was how a situation like that was handled.

Answer 4

Yes I had something similar like this as well, but the professor wants an actual sequence, she said this was too easy that of course that would work. A friend came up with
\[a{n} = (-1,0,1, -2, -1\frac{ 1 }{2 }, -1, -\frac{ 1 }{2}, 0 ... )\]
but I don't understand it....

Answer 5

So it has to be any number L, or just any natural number?

Answer 6

Any real number L

Answer 7

Another friend is trying to use the sequence of
an=tan(n),
but again i'm having a difficult time understanding the subsequence part

Answer 8

u can do this in two ways :-
1-any converges sequences , all its sun sequences also converge :)
2- alternate sequences works as well

Answer 9

all its sub*

Answer 10

I understand that the subsequences of a convergent sequence converges as well, but let's say the answer is (1, 1/2, 1/3, 1/4, 1/5,...) I should be able to pick a subsequence that can converge to any real number, therefore the sequence can't be convergent

Answer 11

ok if u take 1/n as a sequence then follow this :-

1/2n is a subsequence from 1/n which conv 0
1/n^2 also a subsequence which converge to something (12/pi as i think , not sure
any infinitly many examples

Answer 12

ok i got what u mean , take something with respect to L :)
1/n + L

Answer 13

Ha, I tried that before, the professor no dice, it has to be an actual sequence

Answer 14

1+nL /n

Answer 15

As far as I've seen, you can only get specific subsequential limits as answers if those values repeat themselves or are actually limits. So what you started typing up would only have a limit of 0. But if you have a sequence like (1, 2, 3, 1, 2, 3, 1, 2, 3, ...), then you have 1, 2, and 3 as subsequential limits. The subsequences you would choose to state that they are subsequential limits would be \(a_{3m-2}\ = 1\), \(a_{3m-1}=2\), and \(a_{3m}=3\). So somehow you would have to construct something like that that would converge to all real numbers. If you're not allowed to just to use a second variable, then that seems quite annoying to think of. I'm sure there's some fancy trick, though :/

Answer 16

hmm but u need to consider this :-
if a SEQUENCE is converges then it has only one limit and it cant be variable

Answer 17

Yeah, when she goes over this in class, there's going to plenty of us upset of how easy it was

Answer 18

@ikram002p the sequence does not need to be convergent. It's just a sequence that if I have a number L, i can make a subsequence that converges to L

Answer 19

ugh lol
i had problem in understanding ur question xD
first i thought as what u said , then u said something about L
so i thought its like this :-
any subseq , is converge to any real L

Answer 20

haha, yea i know it's a tricky question. I really dislike my professors worksheets. Thanks for trying everyone.

Answer 21

any order group , satisfy what u need :)
take rational numbers for example , integers, ....

Answer 22

Ive had my share of anger because of my analysis professor this semester, too. Sucks. I'm definitely learning, but I know I'm dealing wih more frustration than needed -_-

Answer 23

rational number is a good example :)

Answer 24

oh i like my proffesors xD

Answer 25

Haha, I dont like any of my math ones.

Answer 26

:O whats ur majors guys ?
and what courses u taken ?
i'd like t help or talk about anything pure math xD

Answer 27

I'm a Math Major, I only have this class and History of Math and I'm done

Answer 28

Math major. Im in real analysis and abstract algebra. Getting my butt kicked because of my professors. Analysis is difficult, but ive grown to dislike my professor in that course. Abstract is easy until you take an exam x_x

Answer 29

and in regards to my Prof. I like most of them, but I find this professor makes her worksheets incredibly difficult

Answer 30

haha I feel you about Abstract Algebra

Answer 31

haha lol we are all in same bout XD im math major as will
this semester i have topology and regression analysis then graduate :P

Answer 32

The difficulty of hw has nothing to do with my dislike of my analysis professor. All he does is regurgitate notes, only go to class because its required. Had an exam on Monday for analysis and it had one faulty question and one intentional trick question :/ Wasted so much time on a question that was tricking us and didnt even get to finish my exam because of the time spent on that one question.

Answer 33

i love abstract algebra :O and real analysis

Answer 34

nerd

Answer 35

I'm more a fan Euclidean Geometry and the Calculus'

Answer 36

@bibby aren't we all.... look where we are at haha

Answer 37

haha geometry is soo good course :)
where are u from ?

Answer 38

Abstract is easy until an exam, lol. The concepts are all easy for the most part, but then the exams are more proof heavy or I just forget how to do something. I had that today, forgot how to do some problems and then didnt know how to do a proof x_X

Answer 39

haha, just joking around with ikram @angmarti87

Answer 40

yeah , well in exams its like too many questions for everything :D

Answer 41

I'm from California, I go to California State University of Bakersfield

Answer 42

bib lol im a nerd yes :P

Answer 43

I too have a problem with finishing I always get to the last question but never finish it. It's happened the past 2 exams

Answer 44

im from Palestine , i go to AAUJ ,
nice to know some math majors here xD
*tears *

Answer 45

I wish Id have known an easier way to do the problems on the exam, though. I need to look at my textbook and find the easier ways for proving isomorphicm, too, lol. The test had me paranoid that I had to do it a certain way ._. And I'm definitely a nerd. Ill "take a break" from studying for my biology class by helping other people do calculus or whatever other math. I think it takes a nerd to do math when theyre taking a break, lol.

Answer 46

Palestine is not a country

Answer 47

as far as i know...

Answer 48

lol @angmarti87 it happens all the time xD
number theory and abstract algebra have heavy exams

Answer 49

wow @ikram002p what time is it over there?

Answer 50

its 8:15 im im sort of late xD
nice talking and knwoing u lol both @angmarti87 and @Concentrationalizing

Answer 51

AM

Answer 52

Wow your a whole day ahead of me..... Take care

Answer 53

Yeah, 11:18pm here x_x

Answer 54

Same here @Concentrationalizing Pacific Time

Answer 55

Yep, yep. But while Im on here, I might as well ask about one of the questions on my abstract exam from today, lol.

Answer 56

Sounds like a plan