Skip to content
By using Twitter’s services you agree to our Cookies Use. We and our partners operate globally and use cookies, including for analytics, personalisation, and ads.

For the best Twitter experience, please use Microsoft Edge, or install the Twitter app from Microsoft Store.

  • Home Home Home, current page.
  • About

Saved searches

  • Remove
  • In this conversation
    Verified accountProtected Tweets @
Suggested users
  • Verified accountProtected Tweets @
  • Verified accountProtected Tweets @
  • Language: English
    • Bahasa Indonesia
    • Bahasa Melayu
    • Català
    • Čeština
    • Dansk
    • Deutsch
    • English UK
    • Español
    • Filipino
    • Français
    • Hrvatski
    • Italiano
    • Magyar
    • Nederlands
    • Norsk
    • Polski
    • Português
    • Română
    • Slovenčina
    • Suomi
    • Svenska
    • Tiếng Việt
    • Türkçe
    • Ελληνικά
    • Български език
    • Русский
    • Српски
    • Українська мова
    • עִבְרִית
    • العربية
    • فارسی
    • मराठी
    • हिन्दी
    • বাংলা
    • ગુજરાતી
    • தமிழ்
    • ಕನ್ನಡ
    • ภาษาไทย
    • 한국어
    • 日本語
    • 简体中文
    • 繁體中文
  • Have an account? Log in
    Have an account?
    · Forgot password?

    New to Twitter?
    Sign up
solifine's profile
solifine
solifine
solifine
@solifine

Tweets

solifine

@solifine

in my house we have jump scares

phck.net
Joined November 2019

Tweets

  • © 2020 Twitter
  • About
  • Help Center
  • Terms
  • Privacy policy
  • Imprint
  • Cookies
  • Ads info
Dismiss
Previous
Next

Go to a person's profile

Saved searches

  • Remove
  • In this conversation
    Verified accountProtected Tweets @
Suggested users
  • Verified accountProtected Tweets @
  • Verified accountProtected Tweets @

Promote this Tweet

Block

  • Tweet with a location

    You can add location information to your Tweets, such as your city or precise location, from the web and via third-party applications. You always have the option to delete your Tweet location history. Learn more

    Your lists

    Create a new list


    Under 100 characters, optional

    Privacy

    Copy link to Tweet

    Embed this Tweet

    Embed this Video

    Add this Tweet to your website by copying the code below. Learn more

    Add this video to your website by copying the code below. Learn more

    Hmm, there was a problem reaching the server.

    By embedding Twitter content in your website or app, you are agreeing to the Twitter Developer Agreement and Developer Policy.

    Preview

    Why you're seeing this ad

    Log in to Twitter

    · Forgot password?
    Don't have an account? Sign up »

    Sign up for Twitter

    Not on Twitter? Sign up, tune into the things you care about, and get updates as they happen.

    Sign up
    Have an account? Log in »

    Two-way (sending and receiving) short codes:

    Country Code For customers of
    United States 40404 (any)
    Canada 21212 (any)
    United Kingdom 86444 Vodafone, Orange, 3, O2
    Brazil 40404 Nextel, TIM
    Haiti 40404 Digicel, Voila
    Ireland 51210 Vodafone, O2
    India 53000 Bharti Airtel, Videocon, Reliance
    Indonesia 89887 AXIS, 3, Telkomsel, Indosat, XL Axiata
    Italy 4880804 Wind
    3424486444 Vodafone
    » See SMS short codes for other countries

    Confirmation

     

    Welcome home!

    This timeline is where you’ll spend most of your time, getting instant updates about what matters to you.

    Tweets not working for you?

    Hover over the profile pic and click the Following button to unfollow any account.

    Say a lot with a little

    When you see a Tweet you love, tap the heart — it lets the person who wrote it know you shared the love.

    Spread the word

    The fastest way to share someone else’s Tweet with your followers is with a Retweet. Tap the icon to send it instantly.

    Join the conversation

    Add your thoughts about any Tweet with a Reply. Find a topic you’re passionate about, and jump right in.

    Learn the latest

    Get instant insight into what people are talking about now.

    Get more of what you love

    Follow more accounts to get instant updates about topics you care about.

    Find what's happening

    See the latest conversations about any topic instantly.

    Never miss a Moment

    Catch up instantly on the best stories happening as they unfold.

    solifine‏ @solifine 31 Dec 2019
    • Report Tweet

    A group is a set with a distinguished element e and a binary operation [ , ] satisfying: ‣ [a,b] = [[a,c],[b,c]] ‣ [a,e] = a ‣ [a,a] = e for all a,b,c.

    8:25 AM - 31 Dec 2019
    • 51 Retweets
    • 307 Likes
    • michael bloombert dog girl queen John Malkovich HoTT takes Charlie Schlinkert Srinivas Rau FractalEncrypt Évariste ∆-module
    9 replies 51 retweets 307 likes
      1. New conversation
      2. John Carlos Baez‏ @johncarlosbaez 31 Dec 2019
        • Report Tweet
        Replying to @solifine

        Nice! To make this familiar to the unwashed masses, write [a,b] = ab^{-1}.

        3 replies 0 retweets 43 likes
      3. solifine‏ @solifine 31 Dec 2019
        • Report Tweet
        Replying to @johncarlosbaez

        Yeah for the rest of the year, I'm only going to think about division! Goodbye, multiplication and composition.

        2 replies 1 retweet 17 likes
      4. 3 more replies
      1. New conversation
      2. Heteroclitus Maximus‏ @RangaTheDude Dec 31
        • Report Tweet
        Replying to @solifine @vikasF22

        Form a ring with one more operator.

        1 reply 0 retweets 1 like
      3. solifine‏ @solifine Dec 31
        • Report Tweet
        Replying to @RangaTheDude @vikasF22

        I suspect there's nothing interesting to do for the ring multiplication, because this definition really relies on having inverses. But one thing you'd want to do anyway is express the notion of "abelian group". The best I can do is ‣ [a,b]=[[e,b],[e,a]]

        2 replies 0 retweets 2 likes
      4. 2 more replies
      1. New conversation
      2. Francis‏ @Francis16833887 Jan 1
        • Report Tweet
        Replying to @solifine

        It looks like you can reduce the axioms further to the structure of the division map [ , ] subject to the axioms that [a,b] = [[a,c],[b,c]] and that all [a,a] are equal to a single element.

        1 reply 0 retweets 0 likes
      3. solifine‏ @solifine Jan 1
        • Report Tweet
        Replying to @Francis16833887

        solifine Retweeted solifine

        I don't know how you'd get out of insisting [a,[a,a]]=a. But otherwise it's fine to do this… that's how it is presented in Hall's book actually.https://twitter.com/solifine/status/1212064308311609345 …

        solifine added,

        solifine @solifine
        Replying to @solifine @johncarlosbaez
        All of this is derived from Marshall Hall, Jr., The Theory of Groups (1959). Well, except the part showing [c,b] = [b,c]⁻¹, which is an axiom there (whereas [a,a]=e doesn't appear).
        2 replies 0 retweets 1 like
      4. 2 more replies
      1. New conversation
      2. JohnMeuser‏ @JohnMeuser Jan 1
        • Report Tweet
        Replying to @solifine

        @johncarlosbaez can mention of the identity element be dropped with these three equations? [a,b]=[[a,c],[b,c]] [a,[b,b]]=a [a,a]=[b,b] What do we get with just [a,b]=[[a,c],[b,c]] [a,[b,b]]=a ?

        2 replies 0 retweets 1 like
      3. John Carlos Baez‏ @johncarlosbaez Jan 1
        • Report Tweet
        Replying to @JohnMeuser @solifine

        Yes, you can drop mention of the identity as mentioned. In group theory there's a famous easy proof that if ax = a for all a and ya = a for all a then x = y, so if there are right units and left units they must all be equal.

        2 replies 0 retweets 2 likes
      4. 1 more reply
      1. Shahid Nawaz‏ @NawazSnafridi Dec 31
        • Report Tweet
        Replying to @solifine

        What notation is this?

        0 replies 0 retweets 1 like
        Thanks. Twitter will use this to make your timeline better. Undo
        Undo
      1. Pavel Roskin‏ @pavelroskin Dec 31
        • Report Tweet
        Replying to @solifine

        Easy to show on a Rubik's cube. Any combination of moves is a group element. The comma is performing the first operand, then _reverting_ the second operand.

        0 replies 0 retweets 0 likes
        Thanks. Twitter will use this to make your timeline better. Undo
        Undo

    Loading seems to be taking a while.

    Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.

      Promoted Tweet

      false

      • © 2020 Twitter
      • About
      • Help Center
      • Terms
      • Privacy policy
      • Imprint
      • Cookies
      • Ads info