Boundary of an Open Ball - Metric Spaces

2021.10.26 09:32 Sazzo100 Boundary of an Open Ball - Metric Spaces

Hi everyone, I have a question on metric spaces here. I've put my thought process at the bottom and any help is appreciated :)!
Q: Let (X, d) be an arbitrary metric space. Show that any point x belonging to the boundary of the open ball B(x_0, r) must satisfy d(x_0, x) = r.
THOUGHTS: We know from the definition of an open ball that it does not contain the boundary points so for r to be on the boundary d(x_0,x) >= r but I'm not sure how to show that it cannot be greater than r. The question is very obviously true in my head but I don't know how to write it mathematically.
Thanks in advance!
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2021.10.26 09:32 BottleWonderful5754 Electrician job

I am from Nepal and want to do a job abroad. How can I get a job in the USA, Canada, Australia?
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2021.10.26 09:32 RatProphetist My terrible taste, mock me, or recommend me things.

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2021.10.26 09:32 Ksm-official It's a Pirates Life For Me | Assassins Creed Black Flag 2021

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2021.10.26 09:32 Zane_isnt_my_name I wish these were his stone ocean colors

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2021.10.26 09:32 buckaroot_ nice one king

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2021.10.26 09:32 Pokemon__50 BabyEmperorFloki $BEF | Whitelist Presale 30 October 6 PM UTC| Sweepwidget competition LIVE | 5% Doge Rewards | x100 potential | to Mars & beyond 🚀

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2021.10.26 09:32 thebarberwhogames My Silent Hill collection, (still need to find the Vita game at some point)!

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2021.10.26 09:32 chucky_cakes [17F] hello, i enjoy horror and rap, love sublime & three 6 mafia, into gore and hippie shit & want a sincere connection wit someone hmu🌝

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2021.10.26 09:32 theoryofdoom River North Stabbing Victim Questions Suspect's Release, State's Attorney Responds

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2021.10.26 09:32 RepublicTexas1836 Article on planned 5th Ave busway

https://www.nytimes.com/2021/10/26/nyregion/fifth-ave-bus-deblasio.html
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2021.10.26 09:32 logfromrenandstimpy User & Post Flairs + Rules

Alright donks, the user flairs have been curated and are now available. I didn't post every suggestion just so it's not a list of 100+ flairs, but maybe we can do some betting system similar to what MMA does I'm the future to get users more personalized flairs.
Also, we created some post flairs to try and organize the subreddit. The two flairs that you guys will use the most are "Donk Shit", which is for good faith discussion about the show, subreddit or the hosts in general, and "Gas Station Food" which is designated for shit posts. If your post isn't in good faith then more than likely it's a shit post.
Lastly, we are going to be coming up and implementing some sub rules soon. Nothing crazy, just the normal rules you see on almost every sub. We have already established that unrelated post, like the TFATK posts, will be removed, but we've also gotten antisemitic posts directed at Ariel and posts using mentally handicapped as jokes. Make fun of Ariel for his plethora of shows, make fun of donks for their lame Fan Submission pictures, but use your brain and know their is a line. Racism, bigotry, homophobia, and hate speech of any kind will be removed and result in a ban if you can't get your shit together.
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2021.10.26 09:32 Nosrac2002 Join

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2021.10.26 09:32 Stillbutters Does anyone ave a good maxis match furniture cc folder?

ive been trying to find a cc folder for maxis match furniture but i cant seem to find any good ones below 4GB atleast or around that
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2021.10.26 09:32 azasimagrisizbasim !

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2021.10.26 09:32 drup00 has anyone notice valravn spells Ohio

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2021.10.26 09:32 portalrbn Banda lança EP e clipe com temática escolar mesclando conteúdo da sala de aula com a musicalidade do pagode

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2021.10.26 09:32 SchildwachePotsdam Getting quicker with thrusts and strikes from below?

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2021.10.26 09:32 Acceptable-Ad5944 Ain't Done Nothing If You Ain't Been Called A Red (Live / 1984)

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2021.10.26 09:32 Jsiwowo92938381ejsj Quick Random Question

I have an infection that seems to be coming back after 2 runs of antibiotics, my GP said I should maybe meet with a surgeon to see.
Does this mean I definitely need surgery or do surgeons also just look at things etc?
21, 178cm, 168lbs, Male, non smoker, had previous infection that went away with antibiotics twice, but returning again from pilonidal cyst
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2021.10.26 09:32 RadiantWarriorOfUrka Cursed Cat In The Hat

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2021.10.26 09:32 Puzzled_Thing1992 Looking forward to saying goodbye to another zero! Love this! Lets gooo!

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2021.10.26 09:32 ramjuly8904 indian crow

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2021.10.26 09:32 MaTRESHkaRus Evolution of the Ivolga trains in Moscow (Russia). You can turn on subtitles

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2021.10.26 09:32 PrestigiousHumor5402 Ruv.

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