Just want to point out, the last example is also an example of a set with a binary operation that is associative but NOT commutative.
Let G = $\mathbb{Z}$, and let $*$ be the following operation.
$*:\mathbb{Z} \times \mathbb{Z}\rightarrow $ given by $x*y = x$
 Take $\forall x, y, z\in \mathbb{Z},
 (x*(y*z)) = x*y = x ((x*y)*z) = x*z = x$
$\therefore$ associative.
 But, $x*y = x \neq y*x = y$
Hence it is associative but NOT commutative.

i'll convert this later for anyone interested *lol* just gna dump this here first

edited:
oooo latex is working on blogger ITS BEAUTIFUL

i like to study

because studying is a form of escape. (so gay)
but sometimes when i see stuff i don't like, i just stop, and start studying instead. really avoiding reality by studying (how ironic).
have also been listening to some dude's emo song on replay. let me check.
i've played it 13 times.

i'm avoiding ... losses stirred emotions reality burdens self-doubt despair (there should really be commas,)

sunday
decided to pack my room, because new macbook means u need to pack your room to feel new.
cleared out my cupboard, and i found my math work from sec sch.
it was really damn sick i swear i had/did so much math stuff like...... 4-5 times any other subject **LOL**.  and i was really pretty damn good at math. what happened. lolololol. uni happened.

FOR ENCRYPTION

yo
http://www.vincentcheung.ca/jsencryption/
use this to encrypt stuff. just a reminder to myself *lol*

WOOHOO
i m v happy
coz i'm blogging in bed.
u don't understand. **lol**.
i got a new macbook and i no longer need to be connected permanently to a power source woohoo.
i also bought a new pair of nike dunk sky hi in black so pretty and at $20 cheaper than its sale price *LOL* and i had my queensway curry chicken today i am happy
aud came with me to lecture. it was fun. HAHA.
alright. cs is still annoying *lol* but gna roll around for a bit

general elections

i have no comments.
i'm a very .... well i'd like to say passive but also not true *lol* i guess it just doesn't feel like a big enough concern to me so.. i don't rly care **lol**  i know i should hahahah but. idk. just no opinions or whatever thoughts. anyone is fine. hahaha.

ok i need to settle sep shit.

like very long nv blog *lol*
let me see if i have nice photos to upload.

ok don't have sad.

anw. enjoying school recently.
like the past week/last week.
the first two weeks were quite bad. i think i studied more then *LOL*.
maybe because i've been going out a bit these two weeks.
but really, thank God for His peace and strength to make it through my school days and still enjoy studying. i really feel so glad and joyful when i understand my math lectures **lol**. also when i am not tired i am very happy coz its rare hahahahah God is good

and i cannot vote.
i m not happy with pap.
i shall cast my hypothetical vote for SDP.