12:20 AM
I reiterate that this sounds a lot more like inverse image than inverse function!

12:45 AM
Yes, when applied to sets vs elements, it is. That is why $\overbrace{f^{-1}(\{1\})}^{\emptyset}\ne\overbrace{\ f^{-1}(1)\ }^{\text{doesn't exist}}$, if an inequality can be applied to something that doesn't exist.

Ah I see, so I missed the difference between inverse of an element and function
Sorry I was away for a while, just saw your responses
Thank you for the clarifications!

you're welcome. i was very happy to help.

@robjohn is there a cheat sheet for stuff like the recent comments above?

Hi ! I have a group G of order 60 which has a homomorphic image of order 12 that is cyclic then what is the order of normal subgroups that G has?
What I know is that all subgroups of the image will be normal (as the image is cyclic) and so their pullback (pre-image) will be normal.
But what confuses me is this: if $\xi: G\to G’$ is a homomorphism and let $K\le \xi (G)$ then what happens to the order of $\xi^{-1}(K)$
Note: $\le$ is symbol for subgroup here.
Background: page no. 218 in an example in the paragraph following theorem 10.4 in Gallian’s abstract algebra.
According to me: 5,10,15,20 and 60 are the possible orders of normal subgroups of G if they exist at all.

1:23 AM
@leslietownes smack
That’s the symbol for normal subgroup. What is the order of the preimage of $K$ In terms of the order of $K$?

Hi, Ted. For normal subgroup I use left triangle symbol.

Everyone has different symbols.
Anyhow, what are the possible orders of subgroups of a cyclic group of order 12?

yeah. possible orders for subgroups of cyclic group of order 12 are precisely the divisors of 12: 1,2,3,4,6,12

Now why do we multiply these all by 5?

Ted, I know that G/kernal is isomorphic to $\xi (G)$ so kernal has order 5 and is normal.
But I don’t understand why we should multiply by 5.

1:33 AM
Fundamental Homomorphism Theorem.

@TedShifrin I’m confused here. I tried to show that per-image of K and K have the same order but got stuck as the mapping is onto but may not be one one.

Huh?
Of course it’s not 1-to-1 if there’s a kernel of order 5.

Right. So 5 elements of G are mapped to only 1 element in $\xi (G)$
@TedShifrin I don’t understand this :’(

You just explained it. Apply it to the preimage of any subgroup.

Hmm. I’m getting there but not quite there. I’ll think more on this. Something came up so for now, I must leave. Bye Ted. Take care. I’ll get back to you soon :-)

1:46 AM
Tata.

2:29 AM
i was on the phone with someone from work and my daughter demanded to get on the phone. she told a nonsensical story about ducks and opossums. then she said she played at school and was going to get a vaccine. in response to questioning about vaccines my daughter handed the phone back, asking, "can you talk to her?" really loudly.

2:46 AM

@leslietownes sounds like they’ll fire you within the week.

3:17 AM
that'll mean more of me around here. stay tuned

i'm awaiting the consequences

I'm still stuck at the question of normal subgroups :'(
@Koro so how does that give me normal subgroup in G?

just be prepared for a math problem at work @leslietownes .

we had one the other day. people kept going back and forth about 37% being the maximum of something. it came up. it related to the poisson distribution and the probability of the count being 1. conversation came to a standstill when someone said, let's ask leslie townes, he knows about this.
i said, oh, did you mean 1/e? yes, i guess that rounds up to 37%.
cue laughter and change of subject
the two things that have come up in my real life non math job: poisson distribution (2x), convolution of compactly supported smooth functions (?????? 1x)
nothing else.

3:36 AM
@leslietownes are you in a tech focused legal office?

broadly speaking, yes. most of what i do is legal and not tech.

I like how Leslie never uses uppercase letters :-)

I'm just trying to conisder plausable scenarios for the earlier statement

the convolutions thing was kind of interesting. we wanted to show an invention should not have been patented. it talked about waveforms. earlier-published papers described the design of devices, but not how they functioned in reality. in particular, no graphs of waveforms.
so someone needed to argue to the patent office, if you turned this design on and put this input in, you'd get this waveform out. that was me.

I feel like I encountered a whole load of problems that may have been solved as vector gemoetry problems as a mechanic, but trying to actually come up with an analytical solution for a task that is "best" solved by trial and error would not make my then boss happy

3:40 AM
i remember the first time i used math. a storm had blown down the TV antenna on our roof, and we needed to secure the new antenna with wire, and because it was precarious (the roof sloped somewhat) my dad didn't want to carry up more wire than he needed.

Nice!, My partner wants to go into IP law, once she finishes her thesis, and provided she isn't deported before then

so it fell to me to use trigonometry to figure out how much wire we needed to secure the pole for the antenna, plus some extra for tying off.
andrew it is nice work if you can get it.

Haha, my Dad on the other hand would never trust me with geometry, he considers himself somewhat of an expert

my calculations were right, too. that was the first time i remember seeing math validated in real life.
we pulled the wire taut and had about a foot to spare, just like i'd said we would.
i miss tv antennas. we had this cool little console in our living room you could use to rotate the antenna. it pointed at san francisco.

Nice. And then some shmuck in the back row is like :When are we ever going to need this in real life
that sounds like a full on radio dish.

3:44 AM
the ignorance behind that question has never ceased to amaze me.
if i could go back and time, what would i tell myself? "learn enough trigonometry to tie down a tv antenna, and also the poisson distribution, and convolution of smooth functions?"
life doesn't work like that.

@leslietownes its a blissfull life for some
I kinda want to go back to highschool when my friends started asking that question and point out that the opportunity cost of ignorance is far higher than the cost of learning seamingly irrelevant things.

people tend not to subject all subjects to that level of scrutiny. i don't need to know the contents of basically any book that was ever written on the job. i don't need to know history on the job. the job is largely just being sensitive to the requirements of people who are more powerful than i am.
it's like scrabble. you rarely use Q or Z. you still ought to know them.
i don't know.
you'd probably be considered ignorant if you didn't know history or the contents of any book after 1800. even some science. but with math it is OK.
for more on my nihilistic views, subscribe to my podcast, Leslie Speaks

I'm a bit behind on my podcast listening

i actually have appeared on one podcast once. as a color commentator. it was a weird look into a world of how millennials are trying to handle this media age.

a color commentator? Was it an interior design thing?

3:51 AM
sorry, americanism for 'someone not very expert who is brought on to talk when the experts aren't talking.'
providing 'color' on whatever the actual stuff is.
people work very, very, very hard on stuff that might only get a few hundred listens.
think fred willard on 'best in show.' that was me.

oh, yeah it's crazy the way the listener numbers basically all fall to a small handfull of super sucessfull shows

i mean a few hundred listens x some small amount a month might be someone's rent. but there's an astonishing amount of work going into that stuff, from very professional people.
i live in the LA area, i've had uber drivers that i've seen on TV.
that's actually how i got on that podcast. we were stuck in traffic and got to talking and got suckered into a podcast.

That makes it sound like he was recodording while driving

well we exchanged information at the end. during the drive we got on the phone with her aunt and talked through some issues that had been going on at her acting class.

@Koro That's because leslie's actually an eagle. hyperboleandahalf.blogspot.com/2010/04/…

3:56 AM
shhhh on the internet nobody knows you're an eagle.

@robjohn THanks
a legal eagle?

Exactly

i think he should be known as ip man

hahaha

spent 2+ hrs driving with my 17 yo son around albany/briones today

3:59 AM
why? is he learning to drive?

he's picking it up pretty quickly

if he can do 2 hours in albany he can drive.

yep, gone from zero interest to every day "dad can we drive"

i learned to drive at 20 and then did not step into a car for about 7 years. then my wife had to re-teach me how to drive. that was fun.

daughter started an intership at morgan stanley while she is finishing her exams
i learned around 14 yo
strictly illegal, but mostly rural & low risk
or on private prop

4:01 AM
@PM2Ring Ahahaha nice one!

a lot of nice folks living vicariously through me at the time

i drove just enough to pass my driving test, and the next day i drove from ann arbor to iowa city (about 450 mi on fast interstates). at one point in illinois a gigantic truck merged right into us without seeing us and almost killed us. my fast reflexes saved the day.

wow
i had many miles on sand, dirt, grass
and some pretty heavy duty vehicles

it was funny, i remember cracking open the envelope that had my license inside and handing it to the rental car person.
haha

how naive i was

4:03 AM

i arrived into newark aged 22 and wanted to rent a car. do you have a credit card?
are you over 25?
farm vehicles

i imagine everyone sitting around with hand equipment cutting turf

mostly tractor & trailer
once on a combine
many dumpsters (don't really see these in the us)
have cut & dried turf.

our dumpsters are what they call skips in the UK.
and maybe ireland

actually i am not sure what they are called, they are basically a wheelbarrow with an engine

4:06 AM
the credit card thing is weird. i remember trying to rent a car and i had only cash (more than enough to cover one day of car rental) and a debit card (they could have taken as much as they wanted), but i didn't have a credit card.
but then i said, my mom lives down the road, and they had some exception for locals, so i gave her address and was OK. by the way i could have made up the address, but didn't.

they are a lot of fun, but if you get caught by the gaffer you were in for a beating
luckily i had a gf in white plains, so she rescued me
sadly she left me after a few years, long distance stuff
she used to play field hockey among other things, she was super aggressive.

stay away from those folks

she was great
we made a good orienteering team

there's a place here where if you violate horn not ok then you must give them jaggery (1kg or so) as fine.

haha

4:09 AM
she could whup most guys if it ever came to it

i love the idea of giving stuff that isn't money as a fine

they won't take money only jaggery

my wife has a black belt in some form of karate. she was disqualified from a competition for breaking somebody's nose

that's sweet

that place takes care of injured cows

4:10 AM
i suspect my gf had caused numerous injuries

well i guess it wasn't for breaking the nose, but the way she broke the nose. she was supposed to hold back, or something.

she was very sweet, but you needed to be careful if you crossed her. which i did, of course
another gf used to play camogie, makes lacross look like tiddely winks

one time my wife was sparring with a guy, and had him in a hold where he couldn't move one arm or open his mouth, but he wouldn't give up. so my wife pinched his nose so he couldn't breathe. he gave up
i don't think that's in the karate handbook

she had to leave italy becuase of mafia death threats

i would like to hear more about mafia death threats

4:13 AM
why would mafia threaten the girl?

her bf at the time was a renowned Italian journalist who worked for the Carabiniere & the newspaper Corriera Della Sera against the mafia.

for having too many good ideas
oh god

she was not one to shy away from danger
she was from the north

being a journalist in certain parts of italy ranks only next to being a journalist in russia (or various former republics) in terms of desirability as a career path

she was fiercely republican (you know what i mean)
but also very sweet

4:15 AM
i wouldn't even touch ireland with a ten foot pole on the journalistic front
even today

ironic the whole mafia thing
i'm not sure she got the irony

haha

so i came to berkeley for the quite life
and then nearly lost my friend john hauser

that really sucks

there's lots more, but here is not the apporpriate forum
so much for the quite life

4:17 AM
some day at ben & nicks

absolutely

:-)

people wonder why i am a helicopter dad
you are welcome Koro

i would like to join too:-)

the bar is long enough for everyone.

4:18 AM
i have some nice wine
my wife is making noises of moving to hawaii
i could not live there
i forgot, i meant to order some Gruner Veltliner today

if you move close to the coast in southern california you can get much of the weather without the heightened cost of consumer goods or travel time to other areas.

i would go to MX, but she is concerned

@copper.hat Sorry there isn't more that I know of.

@robjohn i came across some other stuff, but never recorded it
i would like to so to SW MX near the Guatemalan border

i ordered some GV today.

4:22 AM
i think bevmo has some

i would love to move to mexico. some concerns about unrest are valid. frankly living in the USA these days, many concerns about political unrest are valid.

didn't help that we missed being held up in Puerto vallarta by a day

our local bevmo had some of a GV i consider passable but did not have any of my favorites.

and she found out
that was after a day of zip lining with the kids
some serious f*** ziplining i might add
not your american super safe sort of thing

ziplining is a whole lot of fun. i never thought i would enjoy it but i did it once.
like 'hang on or you die" ziplining?

4:23 AM
like is that earth down there?
how am i possibly going to stop in time
i'm not
i had two of my buddy's kids with me too, the parents were working in the bay area so could not come
all young.
but my wife is a bit risk adverse
did you know that linus torvald's wife is a karate black belt?

i did ziplining once from a place which was 10000 ft. above

my wife could take linus's wife.
no question. what form of karate?

wow, 10,000'?

holy f--- koro.

hmm.
which has it

4:26 AM
K2 to everest? or what

@Koro 2 miles high?

i did the annapurna circuit

but they call it by some different name

i chickened out of a victoria falls bungee jump
i met a guy who had done it an hour before i was suppose to jump
his eyes were black & blue and he strongly recommended not doing it
what is the different name @Koro

my company has a 'summer program' where people who might work for the firm try out before their last year of law school and sometimes they organize events for purposes of team building. one time they tried skydiving.

4:29 AM
Copper, it's available at Della adventure park, Lonavala
I still can't recall the name...

while the team was signing up and getting into gear someone ran into the office and announced that somebody had just died skydiving, putting an end to the skydiving that day.
our company does not consider skydiving as an allowable activity anymore

Also, I am trying to verify that 10k ft figure. If I recall correctly that was 10k ft
i am trying to see it on their website
Correction: it was not 10k ft. It was 1250 ft. only. And it's called flying fox there..
:'(

well, falling 1,250' has much the same effect :-)

It's scary when you are the last to go

at 1240 ft, "so far, so good"

4:34 AM
i brought my kids to another zip lining place with all sorts of risky activity but all they cared about was my picking up a chip i dropped in the mud and eating it.

All this ziplining is giving me vertigo.

Have you done swoop ride?

my daughter's new thing at the park that doesn't have the duck pond is going down the slide head-first.
we tell her not to do it, which means that she does it.

did you ever use the slide at cordonices park?

it's falling from 100 ft, out of which 25 ft is free fall.
and then you move like pendulum

4:35 AM
not with my daughter, but yes, i've been on that slide.

@copper When I was a kid.

that slide scare sme

there's another one in oakland that's even better, in my experience. i wonder if it's still there.

i skinned my knuckles on that slide
who makes a slide from concrete?

it's very funny to me that ted, copper's kids, and i have all gone down the same slide.
really cool people, that's who.

4:37 AM
well, you guys are cool, my kids can give you an absolute guarantee of my non coolness
what is a swoop ride?

58428697: depending on how much you weigh time of your ride is determined :-)
They drop you from 100 ft height out of which 25 ft is free fall and then you move like pendulum
That's swoop swing ride

that feels like it might be illegal in this country.

sounds vomit inducing

my wife's uncle validates amusement park equipment for a number of large amusement parks. i'll ask him.

i think great america parkway has something similar

4:40 AM
scary... that's why usually 3 people do it together

my wife's uncles business has two main customers, amusement parks, and the military (think, blast damage to your head as something unexpected makes you accelerate in an unexpected direction). that's all i need to know about amusement parks.
i haven't been on a park ride since maybe age 10. not planning on duplicating the experience.

there's the drop tower in great america parkway, 225' drop
i prefer aerobatics, much more natural

Seems like Europe is not asleep now

4:42 AM
the space he invades, he gets by on you

:58428639: Sorry that was 1250 ft. :'(

:556655664

koro, that's enough to get the job done

:60000000 hi

i get squeamish jumping from a high dive board

4:43 AM
I want to time travel

hehe
I am time travelling rn
At the rate of 1 second per second

i am going at 1 min/min

that's nice, the unit speed parametrization simplifies our formulas considerably

lipschitz joe they call me
some call me rank

4:47 AM
lipschitz joe

lipstick joe

curly joe

i don't mind lipstick as long as someone else is applying it to me
preferably bright red, something subtle
moe?

cauchy joe

my wife is listening to the UCSC orientation vid again, back to the birth control part.
too late for that

4:49 AM
oh god

i am not complete, however
so it is quite possible that i will not converge

a sell job for some health insurance. does the gouge ever stop?????
i am going to make a video about college apps in western europe.
i can see a big business.

say something offensive

score

4:52 AM
copper did you follow that controversy, scandal, whatever about people paying their way into universities here with photoshopped stuff about kids participating in sports

amazing how rife it seems to be

the day that came out was really something around the office, a lot of my coworkers knew those people
and yeah, it apparently is everywhere

i am sad i did not send my son out of country

Breathing is offensive to dead people

i just took an exam and enrolled in the geographically nearest UC
it should be that simple but it isn't

4:53 AM

i have no idea what i'm supposed to do with my daughter. she isn't even 3 but speaks two languages, i feel she's going to need that

everyone is a renaissance child now
my daughter speaks 5, my son 2, myself 0.5
my greek friend speaks about 10
my other greek friend's sister was an eu interpreter
she used to translate for berlusconi, etc
she has some interesting stories
mostly involving viagra, it seems

haha

the vid said unprecedented times