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zepdrix
 one year ago
(Advanced Calculus I) Problem to follow.
zepdrix
 one year ago
(Advanced Calculus I) Problem to follow.

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zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2Suppose that the real number \(\large\rm a\) has the property that for every natural number \(\large\rm n\), \(\large\rm a\le\dfrac{1}{n}\). Prove that \(\large\rm a\le0\).

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2I'm thinking I need to use the Archimedean Property in some way here... struggling with it though... hmm

sohailiftikhar
 one year ago
Best ResponseYou've already chosen the best response.3how it can be true ok take n=5 so 1/5 is not smaller than zero right ?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2If you look at all the fractions on the right side of the inequality, the larger and larger than n gets, the smaller and smaller the fraction gets overall. So it's getting really really close to zero. So a, which is smaller than those set of values has to be zero or below since the fractions take up all of the positives. Conceptually I think I understand. I'm just having trouble proving it XD

sohailiftikhar
 one year ago
Best ResponseYou've already chosen the best response.3oh! yes you can use your word to prove it use them into language of math . just make two equations and draw the conclusion .

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2Do I need to do something with the Completeness Axiom? :o Like if I can show that 0 is the infimum of the set of these (1/n)'s, does that get me on the right track? @zzr0ck3r @ganeshie8 Gotta get the big guns up in hereee XD

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.3This is Archimedes all the way

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.3Suppose \(a>0\), then there exists \(n\) s.t. \(\dfrac{1}{n}<a\) and we are done.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0lol @zzr0ck3r yeah in fact this is the property itself :)

sohailiftikhar
 one year ago
Best ResponseYou've already chosen the best response.3oh yes just suppose a>0 is correct and you will find that this is not correct then a<0 will be correct that's all.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2Suppose a>0, then there exists n s.t. 1/n<a and we are done. Hmm I'm confused... how is that `not correct` though? :o

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.3If you try and use some inf argument, you will end up using the Archimedian property anyway ...I think

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.3Because we were told that \(a<\frac{1}{n}\) for all \(n\).

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2Oh oh oh great stuff! :) For some reason I thought we were contradicting the fact that a>0. Ok ok ok that makes more sense.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0assume a>0, then there exist \(s\in N\) s.t a>1/s , which is a contradiction

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.3yeah, it seems awful circular but it isn't :)

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2Halmos what is that picture? +_+ What is she so exciting about..? Is that... pie?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i felt so but maybe its away to look at it and understand, but i wonder this is not even calculus this is real analysis don't you feel like ur insulting pure math by saying calculus. @zepdrix yeah it is :P i like pies lol

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2Real Analysis? 0_o I've been lied to? Gasp...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0well idk lol it might be just an introduction, im just saying xD

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2Ya, the book is titled "Advanced Calculus, second edition". They're probably just taking it nice and easy this first two weeks of class :)

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.3it is all calculus. what you call calculus some people call baby math. I know profs that refer to 600 level analysis classes as calculus

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.3I would not call this real analysis. I would call it advanced calculus.

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.3My defining line is: when it gets hard :)

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.3even \(\epsilondelta\) continuity/limit proofs I call advanced calculus

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2I'm taking Abstract Algebra I at the same time as this class. That class has me very excited. Such interesting stuff :OOOO

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.3good for you. I much prefer abstract algebra.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0abstract algebra is my favorite topic :D

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.3same, and algebraic topology is the sh*t

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0geometric topology existed me :3 idk im in love with pure math and sucks in applied math xD

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2@Halmos it brought you into existence? 0_o

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.3I have taken general topology and algebraic topology. I start computational topology in the fall. That should either be really cool or super lame.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0hmmm typo excited me xD

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.3three people that hate applied math and love pure math excites me:)

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.3I got pretty liberal with the word hate.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2Ehhh I still love differential equations :) lol

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2And anything with complex numbers gets me all giddy XD

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.3Then you will like analysis once you get used to it. Booooo

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.3jk, I like it as well. I T.A. for that class. I really just hate grading the HW. Group theory HW is fun to grade.

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.3I ta analysis that is...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i like geometry also xD

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.3not difeq, I suck at dif eq. But I once had my class rolling in a difeq class. The teacher was trying to explain something and he said "imagine you had a perfect carpenter" I yelled out JESUS!

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.3I have worked through some of Elements(100 pages or so), but that is about all I know in geometry...

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.3ok back to more fun questions for us @zepdrix

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0well Euclid, Hilbert, spherical,hyperbolic blah blah all kind of geometry i love <3 and @zepdrix yeah share with us :D

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.3Hilbert had his own geometry also. Damn!!! he did that late in the game...

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.3is it just a bunch of hotels in two space? jk

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0well in fact he modified Euclid elements and make it more neat and added most of logical thoughts of it, but its known for most its euclidean only :P

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.3known is a big word :)

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.3p.s. @zepdrix showing that the inf is 0 is a great idea and in general that is what you will be doing, but I don't think you can without the Arch property in this case, or something that needs the arch prop in order to prove it. ..

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.3Also, this could be stronger, change your statement to Suppose that the real number \(a\) has the property that for every natural number \(n\), \(a<\frac{1}{n}\).

Mimi_x3
 one year ago
Best ResponseYou've already chosen the best response.0what math course out there is not hard????
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