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how it can be true ok take n=5 so 1/5 is not smaller than zero right ?

This is Archimedes all the way

\(a\le 0\)

Because we were told that \(a<\frac{1}{n}\) for all \(n\).

assume a>0, then
there exist \(s\in N\) s.t a>1/s , which is a contradiction

yeah, it seems awful circular but it isn't :)

Halmos what is that picture? +_+
What is she so exciting about..?
Is that... pie?

Real Analysis? 0_o
I've been lied to? Gasp...

well idk lol it might be just an introduction, im just saying xD

I would not call this real analysis. I would call it advanced calculus.

hmm

My defining line is: when it gets hard :)

even \(\epsilon-delta\) continuity/limit proofs I call advanced calculus

good for you. I much prefer abstract algebra.

abstract algebra is my favorite topic :D

same, and algebraic topology is the sh*t

geometric topology existed me :3 idk im in love with pure math and sucks in applied math xD

:)

hmmm typo excited me xD

three people that hate applied math and love pure math excites me:)

awesome <3

I got pretty liberal with the word hate.

Ehhh I still love differential equations :) lol

And anything with complex numbers gets me all giddy XD

Then you will like analysis once you get used to it. Booooo

I ta analysis that is...

oh neato :O

i like geometry also xD

wth xD

I have worked through some of Elements(100 pages or so), but that is about all I know in geometry...

\c:

Hilbert had his own geometry also. Damn!!! he did that late in the game...

is it just a bunch of hotels in two space? jk

known is a big word :)

what math course out there is not hard????