Intuitively, a filter on a partially ordered set (poset) contains those elements that are large enough to satisfy some criterion. For example, if x is an element of the poset, then the set of elements that are above x is a filter, called the principal filter at x. (Notice that if x and y are incomparable elements of the poset, then neither of the principal filters at x and y is contained in the other one.)
Similarly, a filter on a set contains those subsets that are sufficiently large to contain something. For example, if the set is the real line and x is one of its points, then the family of sets that contain x in their interior is a filter, called the filter of neighbourhoods of x. (Notice that the thing in this case is slightly larger than x, but it still doesn't contain any other specific point of the line.)
This video is the first part of a two part series about filters and ultrafilters. In this part, I motivate the definition of a filter as a kind of generalization of a point and mention the ultrafilter lemma. Part 2 discusses applications of filters and ultrafilters in topology.
published: 03 Oct 2022
An Introduction to Digital Filters, without the mathematics
In this series on Digital Filter Basics, we'll take a slow and cemented dive into the fascinating world of digital filter theory. Many resources present this topic with dense and exhausting mathematics. Although a fair understanding of complex mathematics is required to fully comprehend the science of filter design, understanding the basics of filters and how they fundamentally work is better left to analysis and visualizations, which I try to do in this series.
Find the full playlist here: https://www.youtube.com/watch?v=Qmd685msY-Y&list=PLbqhA-NKGP6Afr_KbPUuy_yIBpPR4jzWo
References:
Designing Audio Effect Plugins in C++, Will C. Pirkle -
https://www.willpirkle.com/about/books/
Introduction to Digital Filters, Julius O. Smith - https://ccrma.stanford.edu/~jos/filters/
If you've got a...
published: 24 Nov 2022
Filter (mathematics)
If you find our videos helpful you can support us by buying something from amazon.
https://www.amazon.com/?tag=wiki-audio-20
Filter (mathematics)
In mathematics, a filter is a special subset of a partially ordered set.For example, the power set of some set, partially ordered by set inclusion, is a filter.
=======Image-Copyright-Info========
License: Creative Commons Attribution-Share Alike 3.0 (CC BY-SA 3.0)
LicenseLink: http://creativecommons.org/licenses/by-sa/3.0
Author-Info: Pgdx
Image Source: https://en.wikipedia.org/wiki/File:Upset.svg
=======Image-Copyright-Info========
-Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
image source in video
https://www.youtube.com/watch?v=eK5446iarck
published: 22 Jan 2016
LftCM2020: Topology and filters - Patrick Massot
published: 17 Jul 2020
Filter (mathematics) | Wikipedia audio article
This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Filter_(mathematics)
00:00:39 1 Motivation
00:03:43 2 General definition
00:05:56 3 Filter on a set
00:08:56 3.1 Examples
00:12:01 3.2 Filters in model theory
00:12:58 3.3 Filters in topology
00:14:07 3.3.1 Neighbourhood bases
00:14:56 3.3.2 Convergent filter bases
00:17:02 3.3.3 Clustering
00:18:37 3.3.4 Properties of a topological space
00:19:17 3.3.5 Functions on topological spaces
00:21:07 3.3.6 Cauchy filters
00:23:21 4 See also
Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago.
Learning by listening is a great way to:
- increases imagination and understanding
- improves your liste...
published: 15 Jan 2019
Filters-important definitions of filters/topology 2/msc maths
filters - important definitions
topology 2
msc
published: 24 May 2018
state and prove ultra filter principle #topology #importantquestions #mathematics
published: 27 Jun 2023
India vs japan || mathematics challenge || 😅🤣🤣🤭
published: 08 Jun 2021
Bayes theorem, the geometry of changing beliefs
Perhaps the most important formula in probability.
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: http://3b1b.co/bayes-thanks
Home page: https://www.3blue1brown.com
The quick proof: https://youtu.be/U_85TaXbeIo
Interactive made by Reddit user Thoggalluth: https://nskobelevs.github.io/p5js/BayesTheorem/
The study with Steve:
https://science.sciencemag.org/content/185/4157/1124
http://www.its.caltech.edu/~camerer/Ec101/JudgementUncertainty.pdf
You can read more about Kahneman and Tversky's work in Thinking Fast and Slow, or in one of my favorite books, The Undoing Project.
Contents:
0:00 - Intro example
4:09 - Generalizing as a formula
10:13 - Making probabilit...
published: 22 Dec 2019
2- 4.4.3 VSB Mathematics and Explanation of Complementary Filters
This video shows the mathematics behind the need for 'complimentary' VSB filters. The filters work in complement to allow recovery of the original message.
The information in this video will help you understand concepts found in "Modern Digital and Analog Communication" by B.P. Lathi and Zhi Ding.
You can purchase this textbook here:
https://www.amazon.com/Digital-Communication-Electrical-Computer-Engineering-dp-0190686847/dp/0190686847/ref=dp_ob_title_bk
This video is the first part of a two part series about filters and ultrafilters. In this part, I motivate the definition of a filter as a kind of generalizati...
This video is the first part of a two part series about filters and ultrafilters. In this part, I motivate the definition of a filter as a kind of generalization of a point and mention the ultrafilter lemma. Part 2 discusses applications of filters and ultrafilters in topology.
This video is the first part of a two part series about filters and ultrafilters. In this part, I motivate the definition of a filter as a kind of generalization of a point and mention the ultrafilter lemma. Part 2 discusses applications of filters and ultrafilters in topology.
In this series on Digital Filter Basics, we'll take a slow and cemented dive into the fascinating world of digital filter theory. Many resources present this to...
In this series on Digital Filter Basics, we'll take a slow and cemented dive into the fascinating world of digital filter theory. Many resources present this topic with dense and exhausting mathematics. Although a fair understanding of complex mathematics is required to fully comprehend the science of filter design, understanding the basics of filters and how they fundamentally work is better left to analysis and visualizations, which I try to do in this series.
Find the full playlist here: https://www.youtube.com/watch?v=Qmd685msY-Y&list=PLbqhA-NKGP6Afr_KbPUuy_yIBpPR4jzWo
References:
Designing Audio Effect Plugins in C++, Will C. Pirkle -
https://www.willpirkle.com/about/books/
Introduction to Digital Filters, Julius O. Smith - https://ccrma.stanford.edu/~jos/filters/
If you've got any questions, suggestions or recommendations, type them out here, or send me a message on any of my social channels mentioned below.
A lot of time was spent on creating this series, and I plan to do more. So please consider subscribing if you wish to be notified about more releases in the future. And if you feel generous: https://www.patreon.com/akashmurthy
Check out my music here: https://farfetchd-official.bandcamp.com/
Check out the audio track in the intro and outro here: https://soundcloud.com/thrifleganger/tinderbox
Give me a shout here:
Website - https://www.akashmurthy.com/
Facebook - https://www.facebook.com/akash.murthy.319
Instagram - https://www.instagram.com/thrifleganger/
In this series on Digital Filter Basics, we'll take a slow and cemented dive into the fascinating world of digital filter theory. Many resources present this topic with dense and exhausting mathematics. Although a fair understanding of complex mathematics is required to fully comprehend the science of filter design, understanding the basics of filters and how they fundamentally work is better left to analysis and visualizations, which I try to do in this series.
Find the full playlist here: https://www.youtube.com/watch?v=Qmd685msY-Y&list=PLbqhA-NKGP6Afr_KbPUuy_yIBpPR4jzWo
References:
Designing Audio Effect Plugins in C++, Will C. Pirkle -
https://www.willpirkle.com/about/books/
Introduction to Digital Filters, Julius O. Smith - https://ccrma.stanford.edu/~jos/filters/
If you've got any questions, suggestions or recommendations, type them out here, or send me a message on any of my social channels mentioned below.
A lot of time was spent on creating this series, and I plan to do more. So please consider subscribing if you wish to be notified about more releases in the future. And if you feel generous: https://www.patreon.com/akashmurthy
Check out my music here: https://farfetchd-official.bandcamp.com/
Check out the audio track in the intro and outro here: https://soundcloud.com/thrifleganger/tinderbox
Give me a shout here:
Website - https://www.akashmurthy.com/
Facebook - https://www.facebook.com/akash.murthy.319
Instagram - https://www.instagram.com/thrifleganger/
If you find our videos helpful you can support us by buying something from amazon.
https://www.amazon.com/?tag=wiki-audio-20
Filter (mathematics)
In mathema...
If you find our videos helpful you can support us by buying something from amazon.
https://www.amazon.com/?tag=wiki-audio-20
Filter (mathematics)
In mathematics, a filter is a special subset of a partially ordered set.For example, the power set of some set, partially ordered by set inclusion, is a filter.
=======Image-Copyright-Info========
License: Creative Commons Attribution-Share Alike 3.0 (CC BY-SA 3.0)
LicenseLink: http://creativecommons.org/licenses/by-sa/3.0
Author-Info: Pgdx
Image Source: https://en.wikipedia.org/wiki/File:Upset.svg
=======Image-Copyright-Info========
-Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
image source in video
https://www.youtube.com/watch?v=eK5446iarck
If you find our videos helpful you can support us by buying something from amazon.
https://www.amazon.com/?tag=wiki-audio-20
Filter (mathematics)
In mathematics, a filter is a special subset of a partially ordered set.For example, the power set of some set, partially ordered by set inclusion, is a filter.
=======Image-Copyright-Info========
License: Creative Commons Attribution-Share Alike 3.0 (CC BY-SA 3.0)
LicenseLink: http://creativecommons.org/licenses/by-sa/3.0
Author-Info: Pgdx
Image Source: https://en.wikipedia.org/wiki/File:Upset.svg
=======Image-Copyright-Info========
-Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
image source in video
https://www.youtube.com/watch?v=eK5446iarck
This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Filter_(mathematics)
00:00:39 1 Motivation
00:03:43 2 General definition
...
This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Filter_(mathematics)
00:00:39 1 Motivation
00:03:43 2 General definition
00:05:56 3 Filter on a set
00:08:56 3.1 Examples
00:12:01 3.2 Filters in model theory
00:12:58 3.3 Filters in topology
00:14:07 3.3.1 Neighbourhood bases
00:14:56 3.3.2 Convergent filter bases
00:17:02 3.3.3 Clustering
00:18:37 3.3.4 Properties of a topological space
00:19:17 3.3.5 Functions on topological spaces
00:21:07 3.3.6 Cauchy filters
00:23:21 4 See also
Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago.
Learning by listening is a great way to:
- increases imagination and understanding
- improves your listening skills
- improves your own spoken accent
- learn while on the move
- reduce eye strain
Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone.
Listen on Google Assistant through Extra Audio:
https://assistant.google.com/services/invoke/uid/0000001a130b3f91
Other Wikipedia audio articles at:
https://www.youtube.com/results?search_query=wikipedia+tts
Upload your own Wikipedia articles through:
https://github.com/nodef/wikipedia-tts
Speaking Rate: 0.9503992225972198
Voice name: en-GB-Wavenet-C
"I cannot teach anybody anything, I can only make them think."
- Socrates
SUMMARY
=======
In mathematics, a filter is a special subset of a partially ordered set. For example, the power set of some set, partially ordered by set inclusion, is a filter. Filters appear in order and lattice theory, but can also be found in topology from where they originate. The dual notion of a filter is an ideal.
Filters were introduced by Henri Cartan in 1937 and subsequently used by Bourbaki in their book Topologie Générale as an alternative to the similar notion of a net developed in 1922 by E. H. Moore and H. L. Smith.
This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Filter_(mathematics)
00:00:39 1 Motivation
00:03:43 2 General definition
00:05:56 3 Filter on a set
00:08:56 3.1 Examples
00:12:01 3.2 Filters in model theory
00:12:58 3.3 Filters in topology
00:14:07 3.3.1 Neighbourhood bases
00:14:56 3.3.2 Convergent filter bases
00:17:02 3.3.3 Clustering
00:18:37 3.3.4 Properties of a topological space
00:19:17 3.3.5 Functions on topological spaces
00:21:07 3.3.6 Cauchy filters
00:23:21 4 See also
Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago.
Learning by listening is a great way to:
- increases imagination and understanding
- improves your listening skills
- improves your own spoken accent
- learn while on the move
- reduce eye strain
Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone.
Listen on Google Assistant through Extra Audio:
https://assistant.google.com/services/invoke/uid/0000001a130b3f91
Other Wikipedia audio articles at:
https://www.youtube.com/results?search_query=wikipedia+tts
Upload your own Wikipedia articles through:
https://github.com/nodef/wikipedia-tts
Speaking Rate: 0.9503992225972198
Voice name: en-GB-Wavenet-C
"I cannot teach anybody anything, I can only make them think."
- Socrates
SUMMARY
=======
In mathematics, a filter is a special subset of a partially ordered set. For example, the power set of some set, partially ordered by set inclusion, is a filter. Filters appear in order and lattice theory, but can also be found in topology from where they originate. The dual notion of a filter is an ideal.
Filters were introduced by Henri Cartan in 1937 and subsequently used by Bourbaki in their book Topologie Générale as an alternative to the similar notion of a net developed in 1922 by E. H. Moore and H. L. Smith.
Perhaps the most important formula in probability.
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simp...
Perhaps the most important formula in probability.
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: http://3b1b.co/bayes-thanks
Home page: https://www.3blue1brown.com
The quick proof: https://youtu.be/U_85TaXbeIo
Interactive made by Reddit user Thoggalluth: https://nskobelevs.github.io/p5js/BayesTheorem/
The study with Steve:
https://science.sciencemag.org/content/185/4157/1124
http://www.its.caltech.edu/~camerer/Ec101/JudgementUncertainty.pdf
You can read more about Kahneman and Tversky's work in Thinking Fast and Slow, or in one of my favorite books, The Undoing Project.
Contents:
0:00 - Intro example
4:09 - Generalizing as a formula
10:13 - Making probability intuitive
13:35 - Issues with the Steve example
Thanks to these viewers for their contributions to translations
Gujarati: Hitesh12358, Pragna1991
Hebrew: Omer Tuchfeld
Italian: @crampaldo
------------------
These animations are largely made using manim, a scrappy open-source python library: https://github.com/3b1b/manim
If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own use in mind.
Music by Vincent Rubinetti.
Download the music on Bandcamp:
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown
Stream the music on Spotify:
https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u
If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe
Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3blue1brown
Reddit: https://www.reddit.com/r/3blue1brown
Instagram: https://www.instagram.com/3blue1brown_animations/
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
Perhaps the most important formula in probability.
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: http://3b1b.co/bayes-thanks
Home page: https://www.3blue1brown.com
The quick proof: https://youtu.be/U_85TaXbeIo
Interactive made by Reddit user Thoggalluth: https://nskobelevs.github.io/p5js/BayesTheorem/
The study with Steve:
https://science.sciencemag.org/content/185/4157/1124
http://www.its.caltech.edu/~camerer/Ec101/JudgementUncertainty.pdf
You can read more about Kahneman and Tversky's work in Thinking Fast and Slow, or in one of my favorite books, The Undoing Project.
Contents:
0:00 - Intro example
4:09 - Generalizing as a formula
10:13 - Making probability intuitive
13:35 - Issues with the Steve example
Thanks to these viewers for their contributions to translations
Gujarati: Hitesh12358, Pragna1991
Hebrew: Omer Tuchfeld
Italian: @crampaldo
------------------
These animations are largely made using manim, a scrappy open-source python library: https://github.com/3b1b/manim
If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own use in mind.
Music by Vincent Rubinetti.
Download the music on Bandcamp:
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown
Stream the music on Spotify:
https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u
If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe
Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3blue1brown
Reddit: https://www.reddit.com/r/3blue1brown
Instagram: https://www.instagram.com/3blue1brown_animations/
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
This video shows the mathematics behind the need for 'complimentary' VSB filters. The filters work in complement to allow recovery of the original message.
The...
This video shows the mathematics behind the need for 'complimentary' VSB filters. The filters work in complement to allow recovery of the original message.
The information in this video will help you understand concepts found in "Modern Digital and Analog Communication" by B.P. Lathi and Zhi Ding.
You can purchase this textbook here:
https://www.amazon.com/Digital-Communication-Electrical-Computer-Engineering-dp-0190686847/dp/0190686847/ref=dp_ob_title_bk
This video shows the mathematics behind the need for 'complimentary' VSB filters. The filters work in complement to allow recovery of the original message.
The information in this video will help you understand concepts found in "Modern Digital and Analog Communication" by B.P. Lathi and Zhi Ding.
You can purchase this textbook here:
https://www.amazon.com/Digital-Communication-Electrical-Computer-Engineering-dp-0190686847/dp/0190686847/ref=dp_ob_title_bk
This video is the first part of a two part series about filters and ultrafilters. In this part, I motivate the definition of a filter as a kind of generalization of a point and mention the ultrafilter lemma. Part 2 discusses applications of filters and ultrafilters in topology.
In this series on Digital Filter Basics, we'll take a slow and cemented dive into the fascinating world of digital filter theory. Many resources present this topic with dense and exhausting mathematics. Although a fair understanding of complex mathematics is required to fully comprehend the science of filter design, understanding the basics of filters and how they fundamentally work is better left to analysis and visualizations, which I try to do in this series.
Find the full playlist here: https://www.youtube.com/watch?v=Qmd685msY-Y&list=PLbqhA-NKGP6Afr_KbPUuy_yIBpPR4jzWo
References:
Designing Audio Effect Plugins in C++, Will C. Pirkle -
https://www.willpirkle.com/about/books/
Introduction to Digital Filters, Julius O. Smith - https://ccrma.stanford.edu/~jos/filters/
If you've got any questions, suggestions or recommendations, type them out here, or send me a message on any of my social channels mentioned below.
A lot of time was spent on creating this series, and I plan to do more. So please consider subscribing if you wish to be notified about more releases in the future. And if you feel generous: https://www.patreon.com/akashmurthy
Check out my music here: https://farfetchd-official.bandcamp.com/
Check out the audio track in the intro and outro here: https://soundcloud.com/thrifleganger/tinderbox
Give me a shout here:
Website - https://www.akashmurthy.com/
Facebook - https://www.facebook.com/akash.murthy.319
Instagram - https://www.instagram.com/thrifleganger/
If you find our videos helpful you can support us by buying something from amazon.
https://www.amazon.com/?tag=wiki-audio-20
Filter (mathematics)
In mathematics, a filter is a special subset of a partially ordered set.For example, the power set of some set, partially ordered by set inclusion, is a filter.
=======Image-Copyright-Info========
License: Creative Commons Attribution-Share Alike 3.0 (CC BY-SA 3.0)
LicenseLink: http://creativecommons.org/licenses/by-sa/3.0
Author-Info: Pgdx
Image Source: https://en.wikipedia.org/wiki/File:Upset.svg
=======Image-Copyright-Info========
-Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
image source in video
https://www.youtube.com/watch?v=eK5446iarck
This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Filter_(mathematics)
00:00:39 1 Motivation
00:03:43 2 General definition
00:05:56 3 Filter on a set
00:08:56 3.1 Examples
00:12:01 3.2 Filters in model theory
00:12:58 3.3 Filters in topology
00:14:07 3.3.1 Neighbourhood bases
00:14:56 3.3.2 Convergent filter bases
00:17:02 3.3.3 Clustering
00:18:37 3.3.4 Properties of a topological space
00:19:17 3.3.5 Functions on topological spaces
00:21:07 3.3.6 Cauchy filters
00:23:21 4 See also
Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago.
Learning by listening is a great way to:
- increases imagination and understanding
- improves your listening skills
- improves your own spoken accent
- learn while on the move
- reduce eye strain
Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone.
Listen on Google Assistant through Extra Audio:
https://assistant.google.com/services/invoke/uid/0000001a130b3f91
Other Wikipedia audio articles at:
https://www.youtube.com/results?search_query=wikipedia+tts
Upload your own Wikipedia articles through:
https://github.com/nodef/wikipedia-tts
Speaking Rate: 0.9503992225972198
Voice name: en-GB-Wavenet-C
"I cannot teach anybody anything, I can only make them think."
- Socrates
SUMMARY
=======
In mathematics, a filter is a special subset of a partially ordered set. For example, the power set of some set, partially ordered by set inclusion, is a filter. Filters appear in order and lattice theory, but can also be found in topology from where they originate. The dual notion of a filter is an ideal.
Filters were introduced by Henri Cartan in 1937 and subsequently used by Bourbaki in their book Topologie Générale as an alternative to the similar notion of a net developed in 1922 by E. H. Moore and H. L. Smith.
Perhaps the most important formula in probability.
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: http://3b1b.co/bayes-thanks
Home page: https://www.3blue1brown.com
The quick proof: https://youtu.be/U_85TaXbeIo
Interactive made by Reddit user Thoggalluth: https://nskobelevs.github.io/p5js/BayesTheorem/
The study with Steve:
https://science.sciencemag.org/content/185/4157/1124
http://www.its.caltech.edu/~camerer/Ec101/JudgementUncertainty.pdf
You can read more about Kahneman and Tversky's work in Thinking Fast and Slow, or in one of my favorite books, The Undoing Project.
Contents:
0:00 - Intro example
4:09 - Generalizing as a formula
10:13 - Making probability intuitive
13:35 - Issues with the Steve example
Thanks to these viewers for their contributions to translations
Gujarati: Hitesh12358, Pragna1991
Hebrew: Omer Tuchfeld
Italian: @crampaldo
------------------
These animations are largely made using manim, a scrappy open-source python library: https://github.com/3b1b/manim
If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own use in mind.
Music by Vincent Rubinetti.
Download the music on Bandcamp:
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown
Stream the music on Spotify:
https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u
If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe
Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3blue1brown
Reddit: https://www.reddit.com/r/3blue1brown
Instagram: https://www.instagram.com/3blue1brown_animations/
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This video shows the mathematics behind the need for 'complimentary' VSB filters. The filters work in complement to allow recovery of the original message.
The information in this video will help you understand concepts found in "Modern Digital and Analog Communication" by B.P. Lathi and Zhi Ding.
You can purchase this textbook here:
https://www.amazon.com/Digital-Communication-Electrical-Computer-Engineering-dp-0190686847/dp/0190686847/ref=dp_ob_title_bk
Intuitively, a filter on a partially ordered set (poset) contains those elements that are large enough to satisfy some criterion. For example, if x is an element of the poset, then the set of elements that are above x is a filter, called the principal filter at x. (Notice that if x and y are incomparable elements of the poset, then neither of the principal filters at x and y is contained in the other one.)
Similarly, a filter on a set contains those subsets that are sufficiently large to contain something. For example, if the set is the real line and x is one of its points, then the family of sets that contain x in their interior is a filter, called the filter of neighbourhoods of x. (Notice that the thing in this case is slightly larger than x, but it still doesn't contain any other specific point of the line.)