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.
@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.
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 :-)
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.
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)
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
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.
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?"
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 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.
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.
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.
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.
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.
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
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
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 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.
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.
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
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.
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.
copper did you follow that controversy, scandal, whatever about people paying their way into universities here with photoshopped stuff about kids participating in sports
