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Functional Analysis 1 | Metric Space - How to Measure Distances?

📝 Find more here: https://tbsom.de/s/fa 👍 Support the channel on Steady: https://steadyhq.com/en/brightsideofm... Other possibilities here: https://tbsom.de/sp You can also support me via PayPal: https://paypal.me/brightmaths Or via Ko-fi: https://ko-fi.com/thebrightsideofmath... Or via Patreon:   / bsom   Or via other methods: https://thebrightsideofmathematics.co... Join this channel on YouTube:    / @brightsideofmaths   💬 Access to the community forum: https://thebrightsideofmathematics.co... 🕚 Early access for videos: https://thebrightsideofmathematics.co... ❓ FAQ: https://thebrightsideofmathematics.co... 🛠️ What tools do you use: https://thebrightsideofmathematics.co... Please consider to support me if this video was helpful such that I can continue to produce them :) Each supporter gets access to the additional material. If you need more information, just send me an email: https://tbsom.de/s/mail Watch the whole video series about Functional Analysis and download PDF versions and quizzes: https://tbsom.de/s/fa Supporting me via Steady is the best option for me and you. Please consider choosing a supporter package here: https://tbsom.de/s/subscribe 🌙 There is also a dark mode version of this video:    • Functional Analysis 1 | Metric Space ...   🔆 There is also a bright mode version of this video:    • Functional Analysis 1 | Metric Space ...   🔆 To find the YouTube-Playlist, click here for the bright version:    • Functional analysis   🌙 And click here for the dark version of the playlist:    • Functional Analysis [dark version]   🙏 Thanks to all supporters! They are mentioned in the credits of the video :) This is my video series about Functional Analysis where we start with metric spaces, talk about operators and spectral theory, and end with the famous Spectral Theorem. I hope that it will help everyone who wants to learn about it. x 00:00 Introduction into functional analysis 01:49 Metric space (introduction) 02:25 Metric (definition) 03:20 Metric (definiteness) 03:36 Metric (symmetry) 04:07 Metric (triangle inequality) 05:31 Credits #FunctionalAnalysis #VectorSpaces #Mathematics #LearnMath #calculus I hope that this helps students, pupils and others. Have fun! (This explanation fits to lectures for students in their first and second year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)