Mathematics - 2021-06-26 (page 2 of 3)

Aloo Chop (Bengali: আলুর চপ) a snack originating from the Indian subcontinent; in West Bengal and Bangladeshi preparation also widely available in Odisha, it is made out of boiled potatoes and various spices. "Aloo" means potato, and the word "chop" means a small cutlet fritters or croquette in Bengali. It is served hot and warm along with muri (puffed rice), green chilies, and sometimes sauce and salads. It is a vegetarian alternative, and an Indian Bengali equivalent of the aloo tikki. == Variations == In West Bengal there are many types of Aloor Chop. The process of its making and its...

A Stranger

so that next year admission candidate can check this solution and get benefitted

copper.hat

@robjohn that's it!!!

A Stranger

7:08 AM

I like Aloo chop very much.

copper.hat

@AStranger that is very generous of you

A Stranger

This food is very much delicious

copper.hat

I want some now :-)

there is no real street food where i live

in albany california

A Stranger

Please come to bangladesh.

Together we can have some Aloo chop

copper.hat

I would love to. The nearest I have been was Calcutta

A Stranger

7:10 AM

Yup that is in India

our neighbour country

robjohn

@copper.hat there are many recipes online :-)

copper.hat

Well, I guess Siliuiri (?) was the closest i have been

@robjohn my food assembly capabilities are limited

its more fun when there is a little mystery :-)

A Stranger

Yup siliguri is famous for Tea.

copper.hat

I wanted to visit Darjeeling for tea :-)

A Stranger

I like tea, Aloo chop and checkien fry very much

copper.hat

7:13 AM

I love potatoes

A Stranger

Do you take tea?

robjohn

@copper.hat mine are not as varied as I'd like to think, but I get by (or take out)

copper.hat

Ironically associated with Ireland.

@AStranger I love tea. Apparently the Irish & British are the highest per capita tea drinkers in the world

Albeit I do not know how they would know that

robjohn

I don't do coffee, which seems to be what almost everyone drinks in the US. I drink tea.

copper.hat

I drink coffee about 5-6 times per year

A Stranger

7:14 AM

Sylhet of Bangladesh is very popular for Tea

copper.hat

I would love to visit.

I might yet when this silly covid thing quietens down

A Stranger

Can you tell me what is current state of Covid in USA?

Is everyone given vaccines?

copper.hat

i was going to visit a friend in Singapore of my 60th but the covid thing got in the way.

@AStranger Everyone has access to vaccines but not everyone takes them.

A Stranger

When will the universities in the USA are going to start their activities on campus?

robjohn

@AStranger anyone who wants one can get one

copper.hat

7:17 AM

@AStranger I don't know, but I imagine that most will make them available.

A Stranger

ok.

robjohn

@AStranger In the fall quarter, I think most will be back.

copper.hat

@AStranger My 20 yo daughter in London still has no access to vaccine.

My 17 yo son here (albany california) got his months ago.

robjohn

@copper.hat really? That is not good.

A Stranger

Yup. in our country we still have no access in vaccine

Only a small portion has got vaccine

copper.hat

7:18 AM

@robjohn The London thing?

robjohn

yes

A Stranger

Rest of them is still non-vacinnated

copper.hat

@robjohn I am not too worried about her, more the travel practicalities

albeit she has a little asthma thing going on

fingers crossed

robjohn

@copper.hat yes. Flying is chancy if you're not vaccinated

copper.hat

I no longer have relevant contacts in London in the medical community.

I thought her proximity to the AstraZeneca source might ensure quicker distribution but no use...

twitter.com/i/status/1354147044454248449

that's a repost from months ago :-)

@AStranger I suspect by the time I get to Bangladesh you will be in Maryland :-)

A Stranger

7:22 AM

Hopefully

copper.hat

Good luck with it, that's exciting!

wow, its past my bedtime!

A Stranger

Ok. Take care

bye

copper.hat

good night folks! i have to get up early to go for a cycle with a friend :-)

@AStranger Thanks!

A Stranger

Good night

robjohn

Good night. See you later.

Koro

8:58 AM

If I remove finite elements from a dense subset D of $\mathbb R$ then D is dense. How can I got about proving this?

I believe there should be a counterexample to this fact.

lyme

9:53 AM

hello can someone tell where this minus comes from at this question. math.stackexchange.com/q/1533163 ( $-\frac{\pi^2}2f'(x)$

robjohn

10:26 AM

@lyme It might be a typo. Why not ask the poster in a comment?

Koro

11:00 AM

Never mind. I managed to prove the statement: if finite no. of elements is removed from a dense set D then the remaining set D- finite set removed, is dense in $\mathbb R$

Allure

11:17 AM

Quick question: let's say I have a function f(x) and the Fourier transform is g(y). Is there a special name for x, y? Like "Fourier counterpart" or something

wklm

Hi folks! I got the following limes: https://imgur.com/9bPXbQj

And I'm wondering how is it calculated?
any hints?

schn

Dear @copper.hat, could I ask you once more about your notation $\operatorname{sp} \{a(1,2,4)+b\}_{a \in \mathbb{R}}$? Why not specify $b\in \mathbb{R}^3$?

Why only $a\in \mathbb{R}$?

Allure

11:49 AM

Decided to ask question formally =)

Astyx

12:09 PM

@wklm $(1+x/n)^n\to e^x$ for all $x$

To see that take the log, you get $n\log (1+x/n) \sim n x/n =x$. Since $\exp$ is continuous you can take the image, giving you your equality

Sayan Chattopadhyay

Btw @Astyx, Did you understand that intersection proof?

Astyx

I get the proof with specific $p,q,r$

I don't see the relation to this parity thing

Astyx

12:42 PM

Hold on

What about $p=2$, $q=5$ and $r=7$

Largest integer is obviously odd (since 2 is in there)

nvm

Balarka Sen

1:01 PM

You guys are still puzzling over this?

I told you it's not possible to understand algebra

2

Thorgott

1:50 PM

nah, it's the geometry at fault

Adil Mohammed

Helloo

Whats integration of 1/logx?

(I am in high school so do tell me if it involves college level math)

Thorgott

that is known as the integral logarithm

it is not expressible in terms of elementary functions

Alessandro Codenotti

2:10 PM

@BalarkaSen Truth has been spoken

Balarka Sen

Facts don't care about your feelings

3

wklm

thanks a lot @Astyx ! :)

robjohn

@AdilMohammed this answer might be useful. This does use integration by parts.

Balarka Sen

3:10 PM

new The Mountain Goals album is incredible

highly recommend

katrin

3:21 PM

can you ask random math questions here?

hyper-neutrino

@katrin well, it is the math chat room... yes, you can ask random math questions here, though of course there are still minimal quality standards (I think it's significantly more relaxed than main site though)

vitamin d

Can someone please help me to understand how in this paper on page 979 right after equation (36) the error reduces from $O(1/log x)$ to $O(1/log^3 x)$ only by changing a constant?

katrin

@hyper-neutrino okay very clear, thanks

leslie townes

there's a new TMG album? how did i not know?

i think i've seen them live more than any other band. maybe 10 times.

there are minimal quality standards? :)

hyper-neutrino

3:42 PM

well, so i've heard :P

leslie townes

i think the main quality standard is good faith and willingness to listen. the site-specific stuff about PSQs or whatever does not matter so much.

so yeah, i guess there are minimal quality standards.

hyper-neutrino

yeah, seems like it - as long as the asker is showing effort and willingness to learn i think people here are quite helpful and willing to offer assistance

so yeah, some minimal quality standards but i guess more so with the engagement than the actual content itself

leslie townes

yeah. i don't think there is a floor on the abstract 'quality' of the question. there definitely is on main.

partly just because the person is here so you can just ask them to clarify and usually get a decent answer. can't always expect that on the main site.

hyper-neutrino

yeah

and also SE's whole philosophy of a "repository of Q+A intended to help future audiences" isn't really a thing in chat

leslie townes

yeah, this is a repository of nonsense intended to help nobody. if by accident someone gets a question answered, i guess that's cool.

:)

Balarka Sen

4:52 PM

@leslietownes yeah

"dark in here"

released yesterday

Ted Shifrin

Howdy, a @Balarka

Balarka Sen

hi @Ted!

Avra

Hello! Sorry if this question sounds silly, what "Show that for every integer n there is a multiple of n that has only 0s and 1s in its decimal expansion?" means please?

robjohn

Hey, @Ted!

Ted Shifrin

Heya @robjohn

@Avra For every $n$, there is some integer $k$ so that the integer $kn$ has only 0s and 1s in its numeral (no 2s, 3s, etc.).

I saw that recently and didn't believe it.

Avra

5:09 PM

@TedShifrin. Thank you. Do you find this question confusing or not please?

2

Q: Show that for every integer $n$ there is a multiple of $n$ that has only $0s$ and $1s$ in its decimal expansion.

Can anyone please explain this example as I tried a lot to understand it but I can't! The problem: Show that for every integer n there is a multiple of n that has only 0s and 1s in its decimal expansion. The Solution of the book: Let $n$ be a positive integer. Consider the $n + 1$ integers $1,...

Ted Shifrin

No, it seems to give a fine proof.

Note that when you subtract two numbers consisting only of 1s, larger minus smaller, you end up with only 1s and 0s as digits. That's the clever thing.

Avra

So, that is why they took a series of 1's!

Ted Shifrin

Right.

Avra

I somehow get it now!!

Ted Shifrin

Great ;)

Avra

5:13 PM

Because I was wondering, why they did not take another series! Why only 1s

Thank you :)

Ted Shifrin

I'm not clever at this sort of mathematics.

Avra

@TedShifrin. Your explanation suffice. Thanks again

robjohn

@Avra: $\left\{\sum\limits_{j=0}^k10^j:0\le k\le n\right\}$ has $n+1$ elements so two must be equal mod $n$. The difference of these two elements is what we want.

Pigeonhole. Is that what the answer was?

Ted Shifrin

Yes, that's precisely the answer (but it is written with fewer symbols).

Thorgott

5:28 PM

that's clever

Ted Shifrin

Yes. As I said earlier, I'm not clever at this sort of mathematics.

Maybe I'm not particularly "clever" at all.

robjohn

5:41 PM

Oh, that is just a solution from Discrete Mathematics (one of my favorites).

Ted Shifrin

This is something I neither studied nor taught, although of course I know bits and pieces ...

leslie townes

i love that problem.

Thorgott

discrete maths is the last mandatory maths lecture I still need to attend..

Ted Shifrin

@leslie I only recently bumped into it on MSE somewhere.

@Thor Sounds like you're a few years late.

Thorgott

yeah, people usually take it in their 3rd semester

I did not

leslie townes

5:49 PM

discrete math was optional when i was getting a degree. later they scrapped an optional 'intro to proof' class which a lot of people took, which was essentially discrete math, and made discrete math mandatory.

Ted Shifrin

It's definitely closing the barn door long after the cows have left. Maybe you can ask to substitute something more advanced.

At UGA the discrete math course is for CS majors, as it's a bit less proof-intensive than what math majors need from the intro to higher math course.

a @Balarka: Care to elaborate?

leslie townes

that was the issue at berkeley. the discrete math class was not really a proof class. there was some stuff with induction but very formulaic stuff.

but the intro to proof class didn't really have a subject matter. depending on who was teaching it, it was number theory or discrete math. i taught it twice, once each way.

probably better just to have people know discrete math

Ted Shifrin

Yup. In my days, there was no intro to higher math. But then we all discovered we were having to teach the same basics at the beginning of every algebra, analysis, and topology course because you couldn't assume students had those in any order. Plus, ultimately, intro to higher math became a prereq for the proof-based (but not the newer "applied") intro linear algebra.

The bright students don't need the intro to proofs, and I waived it for anyone who did reasonably in either Calculus with Theory or my Multivariable Math course. But plenty of students, even having taken a decent intro to proofs course, still struggle in modern algebra. Analysis is hopeless.

leslie townes

i did like berkeley having intro to proof optional. there are too many nested quantifiers in analysis. and people never get decent experience with inequalities in calculus.

my daughter fell into the duck pond today.

Ted Shifrin

Did the ducks play with her?

How do you "fall" into the duck pond other than walking in?

Balarka Sen

5:57 PM

@TedShifrin If one localizes at a point before taking derivations we still survive, I believe.

leslie townes

there were two new families of ducks since last week. tiny little baby ducks. thankfully they were not nearby. she might have harmed them in struggling to get out of the water. she can't swim.

she was walking alongside it and tripped.

Ted Shifrin

Oh, tripping. I didn't think of that one.

leslie townes

there's a discrete edge. it isn't a natural pond with like a beach part and a slow transition to the pond part. we have one of those too, but we weren't there today. this one is a sidewalk of concrete right up to pond.

some might say that a parent shouldn't let their toddler toddle along the water's edge in such circumstances. we are firm believers in learning from experience.

Ted Shifrin

Head-bashing might be off the list.

leslie townes

we spent about half an hour in the bath afterwards. it's a scummy pond.

i'll sue the city of long beach for the price of three or four capfuls of johnson and johnson 'no more tears' body wash and shampoo.

Balarka Sen

6:01 PM

@TedShifrin I expect the correspondence goes through for Stein domains

We can use exhaustion functions instead of bump functions

Ted Shifrin

Exhaustion functions don't localize, though.

But I thought you might have some comments.

Heading off ...

Balarka Sen

I'll think about it

Balarka Sen

6:18 PM

It seems to be easy to check for domains in $\Bbb C^n$ by Weierstrass preparation theorem

If we do indeed have it for those then the Stein case follows by Cartan theorem B

copper.hat

@schn Sorry, I should have been more explicit. When I write something like $\{f(a)\}_{a \in A}$ I mean the collection of elements $f(a)$ where $a$ takes values in $A$. When I write $\operatorname{sp} S$, I mean the span of the set $S$ which is the collection of all linear combinations of elements of the set $S$ (alternatively the smallest linear subspace containing $S$).

robjohn

@TedShifrin I walked into the local duck pond to help a turtle in distress, but I could imagine tripping and falling in.

leslie townes

there were turtles in the pond, too. more than we had ever seen. none in distress.

robjohn

@copper.hat is that finite linear combinations?

leslie townes

it ought to be.

i put an overline on that if i mean closure of the finite linear combinations in the norm topology.

assuming there is a norm.

copper.hat

6:25 PM

@robjohn yes.

robjohn

@leslietownes We found this turtle on the driveway quite far from its pond. We took it back to the pond and it seemed to have some trouble, so I waded in to help.

copper.hat

I would probably follow the lawyer in this regard.

leslie townes

a few weeks ago we saw some people dumping what was obviously a former pet turtle into the duck pond. that made me sad.

turtles do get big, and they poop a lot. people don't think about that when they get little ones.

robjohn

@leslietownes that sounds good.

copper.hat

I always find helping wild animals puts me in a bit of a conundrum.

leslie townes

6:27 PM

i think in my dissertation i even did something like $\overline{\operatorname{span}}^{\| \cdot \|}$ or something similarly baroque.

copper.hat

I guess the turtle above was domestic.

robjohn

@leslietownes That is how we got our rabbits and one of our dogs. People just discarding them in what looks to be a nice neighborhood (a nice neighborhood with coyotes).

copper.hat

I used $\overline{\operatorname{sp}}$.

I never found a nice, compact, reasonably standard notation for convex cone generated by...

just saying

It always amazes me how selfish people are with domestic animals.

I am in a judgmental mood today.

leslie townes

one of my coworkers works at a rabbit rescue. a lot of her weekends she answers calls and captures domestic bunnies set loose in local parks.

and yeah, coyotes. for heaven's sake.

we have them here and we're nowhere near a wild area.

copper.hat

poor coyotes

robjohn

6:30 PM

I cannot imagine leaving a pet and driving away.

copper.hat

Yup. I agree.

It helps that my closest friend would choose any of his dogs over me if it came to it.

We have been through life & death situations together, but the dogs still win.

leslie townes

my mom had to give up a pet because she couldn't afford its bills. the vet's office told her they would have it as an 'office pet' because they liked it so much. this seemed to me like an updated version of 'your pet is now at home on a farm and has all the space it likes.'

but six months later i went in to settle a bill and there was my mom's cat.

copper.hat

tough one.

robjohn

That's good.

leslie townes

so not everything people tell you is lies. i felt pretty bad about suspecting otherwise after that.

copper.hat

6:34 PM

we never had to deal with exorbitant animal bills

our dog disappeared for 4 days once, we were distraught. we resorted to driving around the countryside, stopping at random places and searching. amazingly we found him on one of the runs. he was feeble and had clearly been an a very bad fight (big 6" gash all the way down to the muscle). took him a while but he bounced back.

leslie townes

oof.

when my parents divorced my dad moved about half a mile away and took our cat. the cat subsequently vanished. he had gone back to sleep in his familiar yard and been adopted by the family that bought the house.

copper.hat

people used to say the cat stays with the house, the dog with the people.

it took me some time to realise that our dog was 'worrying' sheep (that was the term used). it is easy to be blind to your own.

people anthropomorphize animals. dogs have certain instincts that are fairly hard wired. nothing wrong with that, it is nature. owners often need a wake up call.

no convex psqs to be found

trying to work up the energy to go for a ride. my usual buddy was busy this morning.

we usually solve the world's problems once a week

leslie townes

i got all of the exercise i need fishing my daughter out of a duck pond.

copper.hat

it is good to play in mud.

kids need it i think.

leslie townes

she loves dirt, she loves tackling people. we were on a balance beam and she kept jumping off and then doing this weird roll on the grass at the park. i let it all happen.

her immune system is getting a lot of different inputs.

copper.hat

6:47 PM

sounds good to me. i think i was too concerned about my girl and restricted some of her enjoyment

leslie townes

i let my daughter tackle me about 30 times last night. i still hurt from it but she was having so much fun.

copper.hat

now the poor thing is stuck doing an internship for some financial institution.

leslie townes

no!

at least she isn't an attorney (yet)

copper.hat

she would be killer

not in court, but in strategy

has your daughter been to the beach yet?

camping?

do not sign her up for girl scouts (the cookie sort)

leslie townes

we've gone to the beach a few times, mostly pre-covid. she still talks about it. the beach tends to have a lot of crazies. she has not been camping, and knowing her mother, never will be.

definitely no scouting.

copper.hat

6:50 PM

i think camping would be good for her

monoidaltransform

If $F$ is free abelian and $F\cong F' \oplus \mathbb{Z}$ then $F$ is isomorphic to $F'$? where $F'$ is abelian

?

leslie townes

what if F = F' = Z? don't we have a rank problem?

copper.hat

sorry, out of my knowledge base.

leslie townes

oh hrm

i misread the question

if F is Z+Z and F' = Z i think we have a rank problem

monoidaltransform

I'm trying to understand why it follows that $H_0(X)\cong \tilde{H}_0(X)$ from the fact that $H_0(X)\cong \tilde{H}_0(X)\oplus \mathbb{Z}$

leslie townes

6:53 PM

that might be more to do with what H_0 actually is than some fact about free abelian groups.

i'm digging into my mind here, the Z is something from a basepoint? god, my mind is rotten.

monoidaltransform

that's what I thought, but rotman sais that it follows from the fact that $H_0(X)$ is free abelian

leslie townes

rotten, rotman. that can't be a coincidence.

monoidaltransform

you don't like rotman? lol

leslie townes

H_0 is basically the number of connected components of the space? one copy of Z for each? this is 10+ years old stuff for me.

putting up the bat signal for real topologists.

robjohn

@leslietownes what is wrong with camping and scouting according to mom?

leslie townes

7:03 PM

i don't know if she objects to others doing it. she needs to shower upon awakening in her bathroom, and not, some windy state park shower contraption. she thinks of it as unhygienic.

she's also never been camping. i've camped almost everywhere in california, and oregon, and a little bit in canada.

copper.hat

my hip has interfered a bit with my outdoor life, but i think i have some workable solutions.

i still have not been to the top of whitney

leslie townes

i haven't either.

copper.hat

i will, or will die trying

robjohn

Other than when I was in high school or before, I have camped with my wife. When she decided that camping was too hard (sleeping on the ground and being shoved off the air mattress by the dog) we started condo camping.

copper.hat

i like backpacking but my wife not so much

i don't mind the cold. but what she considers cold i consider warm from an outdoor perspective.

leslie townes

7:06 PM

monoidal what section of rotman is this? i think it's pretty standard for the non-reduced thing to be the reduced thing plus Z, i don't know why they'd be isomorphic unless the reduced thing is an infinite sum of Z's already or something. is this a particular space or a general X?

robjohn

@copper.hat I've been as far as one can go on the road. I have not hiked to the peak, however. We will be passing through Whitney Portal on our way to Mammoth next month.

copper.hat

i have some physical constraints now unfortunately, but the 5+ hr drive to from was the main impediment before that

plus the stupid permit thing

i wanted to do the (misnamed) mountaineers route

not climbing, a bit of scramble at the end.

i had to cancel a few trips for family reasons unfortunately

it was also hard to find someone who would go with me. not that that was a constraint, but i like company.

leslie townes

families do get in the way.

copper.hat

i did some climbing with younger folks.

but i do not have the strength & stamina any more

i am not too interested in technical stuff, only if that is the only way to get where i want to go

and it is filled with aggressive annoying types.

leslie townes

a thousand times that.

copper.hat

7:11 PM

who mistake tolerance for unwilling to fight :-)

ok, i need to get off my *

Koro

I rode bicycle (not the motor bicycle) for 60 km once when I was at college. We went to Hajo from my college at Guwahati (30 km apart). What a fantastic day it was!

leslie townes

that's a good bike ride. i don't think i've done more than 15 miles.

copper.hat

I like riding a bike with friends, provided they are not doing a Tour de France

Koro

:-) it was fantastic. and at the destination we had to go ride up a mountain 8km but had no energy left to do that so we returned.

copper.hat

and riding in a pelaton is not fun

leslie townes

7:18 PM

once i biked to the neighboring town. i drove by the place where the windows XP background image of the green hill was taken. i was too tired to bike home but one of my friends had a car.

Koro

else it would have been a 78 km ride :-)

copper.hat

:-) my drug is endorphin

Koro

we started at 7 am and returned by 6:30 pm

I have had some wonderful journeys :-)

@leslietownes windows background image? wow

One of my friends who visited usa recently has been telling how moon looks so much bigger there. Is it true?

robjohn

I don't know if anyone else is interested in astrophotography, but that is one of my hobbies. The annoying thing is that a lot of the others who are interested in it buy all the most expensive equipment and deprecate anything done without such things. I know that the telescope is essential and that needs to be good, but I am also convinced that one can do decent work with a good DSLR, without needing a $20K setup with a dedicated refrigerated CCD camera.

When I show my photos, they complain about how they are not good enough because they know that I have not used one of their whiz-bang astrophoto only cameras.

Koro

whenever some once a 100 years phenomenon happens in the universe that is visible from naked eyes, I always miss to see it :'(

robjohn

7:24 PM

@Koro so you missed the one last night?

Koro

honestly i am not aware if there was such phenomenon yesterday. 😮

robjohn

There wasn't; I was teasing.

Koro

@Rob

copper.hat

@robjohn can you take multiple images and then average the result or some similar processing?

Koro

😁

robjohn

7:26 PM

@copper.hat Indeed

it's called stacking

copper.hat

i'm behind the times

i guess you would need to rotate the camera or something similar to average out camera artifacts?

leslie townes

my wife's uncle is on the board of an observatory and can sometimes sneak people in to use the telescope. it's too cool.

copper.hat

i have a friend who built his own telescope. he ground his own lens. a bit of a fanatic.

thankfully himself & his wife are great cooks with the same degree of fanaticism

Koro

I want to suggest one thing which may be useful to those who are climbing up to 12 km up a hilly area. If there are stairs, they may be shortcuts for you and cut your journey time really short but avoid them else you legs will hurt like anything. The pain is worse than that after taking vaccine

leslie townes

i remember my dad waking me up so we could go look at halley's comet. i remember thinking it was unimpressive and wanting to go back to sleep.

Koro

7:29 PM

i did that once as i thought my mother was lost so I was looking for her. my little sister was with me so I sent her down on a hourse

when i went down the hilly area, my sister waiting there for me. I was not able to walk properly :'(

leslie townes

the covid vaccine?

Koro

and I found out that my mother had reached hotel :-)

@leslietownes yeah

leslie townes

i had the pfizer one. after the first shot i could barely move for a few days. i came on here and bothered people but i couldn't think or work.

robjohn

@copper.hat nah, if there are artifacts, they can be post processed away, but most cameras don't need it.

copper.hat

i suppose you can figure them out by taking a pic of a uniform object

Koro

7:32 PM

for a few days? i thought the side effects last up to only 1 day

copper.hat

what are the limiting factors? atmosphere, radius of lens?

Koro

some people however don't have any side effect though...

copper.hat

my son & i had no side effects. my wife thought she had.

leslie townes

i read somewhere that pfizer #1 can be bad if you've previously been exposed to the virus, which i think i was. i had a two-week period last fall when i couldn't taste anything.

Koro

antibody formation is ensured if there are side effects (according to a video that I watched after taking vaccine)

robjohn

7:34 PM

@copper.hat this image was a stack of 7 images.

leslie townes

there was a lot of covid at my daughter's day care, she probably got it and gave it to us.

i did feel encouraged by the fact that the vaccine had side effects. the second one made my arm hurt. i liked that.

copper.hat

@robjohn nice!

Koro

@robjohn very nice :-)

leslie townes

my wife's uncle would love that.

copper.hat

it bothers me when people think enjoyment is about some extreme (tech, etc.) and have disdain for others who don't share their perspective

robjohn

7:36 PM

For years, I would take one Saturday night a month (new moon) to go to Mt Pinos to take pictures.

leslie townes

i do a small amount of birdwatching and some of the birder community is like that.

Koro

a library has been started here where there are no books but people who share their experience

so you walk in and may be pay something to talk to person to listen to their experience

leslie townes

that sounds dreadful, except, i would like to be one of the people who shares their experience. i could rant about my problems all day.

robjohn

@Koro what, no one records it to write it down in the archives?!

Koro

Mr Rob, I don't know the details. After lockdown, I'll visit it once.

I came to know about it yesterday only :-).

leslie townes

7:39 PM

marina abramovic had something like that in NYC. you could go and just hang out with her. you sat at a table or something. i don't think you were supposed to talk, and she didn't share her experiences, but otherwise it was the same thing.

robjohn

If you look at the image that looks like mine in the wikipedia article, they describe it as "amateur" equipment.

Koro

there people have titles also like: unemployed etc. so you wanna hear a story from the person titled unemployed you can

leslie townes

my dad went and treated it like a staring contest. he lost.

that seems like a cool project. they should record the interactions.

Koro

i thought that the concept was new

leslie townes

my daughter just requested that my wife not reheat the burrito we made for her last night. she wants to have a cold, unreheated burrito. that's my girl.

Koro

7:42 PM

but it already exists somewhere in Denmark

leslie townes

the danes have a way of getting there first.

robjohn

@Koro I was sort of kidding. It sounded like a verbal passage of knowledge, so I had to be techy and want to record it to upload it online ;-)

Koro

where it came first -at Mumbai or in Denmark, I don't know.

robjohn

@leslietownes pizza is good cold, I've never tried a cold burrito. Could be good

leslie townes

oh, they're great.

Koro

7:45 PM

@robjohn I'll find out when I visit it. Probably they do. People would love the videos :-)

robjohn

sure, people today just don't get oral traditions.

Koro

i was working on if 0 is a limit point of the set {fractional part of $\sqrt n, n\in \mathbb N$ }

I chose an arbitrary $\epsilon \gt 0$ and considered the open interval $(0,\epsilon)$ and by Archemedes principal, there exists some N such that $\frac 1N\lt \epsilon$ so if we divide the open interval into N+1 parts, then I thought about applying pigeon -hole principal to fractional parts of $\sqrt n_1,\sqrt n_2,...\sqrt n_N$.

But there is one problem: it is intuitively clear to me that for any two $n$'s (which are not perfect squares), we can't have $\{n_1\}=\{n_2\}$. But I am not able to prove it. Here $\{. \}$ denotes fractional part.

Therefore, I am not able to proceed further with PHP argument.

Transcript for

$Mathematics$ Mathematics