Faust

ah

no i talk to myself all the time

no idea =\

im really not sure who your talking to?

i think it was just as an axiom though

though that was a long time ago.

i think mine was every convergent sequence has a limit in R

its not uncommon, you dont really need it

yes without context every situation is the same i guess.

hes clearly doing an introductory to analysis class not topology though

its pretty hard to claim something with a terminating finite number of terms is irrational

i mean all you need for that is what is a rational or irrational number, if hes not allowed to use that shouldnt be asking a question requiring its definition to be used

that was the point of my example, it doesnt use any tool =p

you dont always need to find the hard answer to things

If someone askes such a silly question as a sequence of rational numbers that converge to an irrational one, no one is stop you from defining a sequence $a_n =$ the first n terms of root 2, each number is rational and the limit is obviously root 2.

There is no reason you can't be creative in mathematics though, alot of times stupidly obvious questions have stupidly obvious solutions.

@obliv do you know what a recurcsive sequence is?

its defintly not what they want you to do though, i am just super lazy

throw in some cleverl use of |a| and your done

it may not be abundantly clear how to find the best upper and lower bound, but finding an upper and lower bound is quite easy without doing any work

i still think its easier to just find the bigger interval directly

thats anthor way of doing it

since you know the sequence is bounded, why bother doing any work?

if U is the upper bound and L is lower bound then $ a, a_n \in [L,U] $ for all n.

@Criggie i mean i am trying to avoid the problem entirely and not do any work at all though

thats not a bounded sequence though

uh i think its technically analysis, but they all blur together for me

@obliv if the set is bounded, just take the closure of the interval of the upper and lower bound, that is a closed set which contains every element of $a_n$ including a.

The friendliness of this chat has seriously deteriorated

i genuinely tried everything and eventually chose to change what i wanted to do based on what i enjoyed doing the most, but yes clearly a cognitive bias i didnt know i had.

@Jakobian My undergrad degree was in physics and biochemistry, i also took classes in psychology, philosophy and statistics. Oddly the only ones i didnt like where classes in statistics, analysis and well PDE's cause who the hell likes pdes.

just cause you are not capable of looking past your inate failings to be objective, please do not subject me to those same standards.

thats your opinion based on no available information, hence the very definition of cognitive bias is what you are hypocritically applying.

I find it amazing that you can claim to have more knowledge about someone you just met than a person who has known them for the duration of that persons life.

@Jakobian so my making a rational choice based on past experiences is because i think less of applied mathematics and thus chose to enjoy them less?

to employ a logical reasoning of selecting things that i more likely to find enjoyable to learn is in no way a means to pat myself on the back. Its just common sense.

@Jakobian the choice was not made because i wanted to avoid anything applied, it was a result of my not enjoying the things that i learned that were particularly applicable outside of mathematics

the sequence need not be an open or closed set, but it certainly is a subset of one.

we arent talking about that set though, we are talking about if that set lay iunside of an open or closed set

though it depends on how you define convergent

not all closed/open sets, but at least one then yes

the key point is "a bounded closed/ open set"

that explains why i hate analysis so much =\

probability theory i got no idea, i tend to avoid anything with stats or thats too applied ^^

which is no way mathematics =p

@Jakobian its very usual in stats

the only other time i can think of measure theory at the undergrad level would be stats lol

are you an engineer?

@SineoftheTime O.o 5th year analysis class for me