Great explanation and visuals. Is there any study done to differentiate sets based on the rate at which they will reach infinity? In your first example, if you define an arbitrary infinity of 100 and assume they both sets get their next value simultaneously, you can show that the multiples of 4 set will reach 'infinity' in 1/2 the time it takes for the evens to reach infinity.
I don't know that your arguments of the speed towards infinity can be made rigorous in any way. Conversely, one could claim that at each finite position of either sequences is the value is finite. It does not really matter whether one is twice as large as the other.
Please help me, how can I synchronise the animations with the audio? What I am thinking is that I should give long pauses by using `self.wait()` and then trim the video according to the narration. I suppose this is not the best method, please share your method if you have better one.
Yes, this is how I do it as well combined with another method: I cut the animation into pieces and vary the speed of the pieces. I think variations between 50 and 200 percent are easily compatible with a decent performance.
github.com/mathelehrer/manim/blob/master/video_cantor/cantor.py I appologize in advance. I'm learning python and manim at the same time. Most parts are most likely rather simple minded and could be done in a more skillful way.
@@Number_Cruncher Aha, your code is so nice to analyze. Hope I will learn something new. Could you explain how you add your voice in the video? Currently, I use shortcut to add voice, but it seems very hard to detect the actual frame to merge the voice. What's your strategy? And yes I subs your channel, Cheers.
I use audacity for recording. Afterwards I apply some noise filters and cut out breaks, that are not needed. For merging audio and video I use kdenlive. Usually, I pause, stretch or compress the video to match with the audio. It is quite tedious, unfortunately.
![Seungmin "그렇게, 천천히, 우리(As we are)" | [Stray Kids : SKZ-PLAYER]](http://i.ytimg.com/vi/kAzmhLHePqU/mqdefault.jpg)
Is that your summarization in the Take-away @10:24? It is a good video on Cantor's work, thanks.
Thank you for your feedback. I should have called it outlook instead of take-away.
Subscribed! This is an interesting take on one of my favorite theorems!
Great explanation and visuals. Is there any study done to differentiate sets based on the rate at which they will reach infinity? In your first example, if you define an arbitrary infinity of 100 and assume they both sets get their next value simultaneously, you can show that the multiples of 4 set will reach 'infinity' in 1/2 the time it takes for the evens to reach infinity.
I don't know that your arguments of the speed towards infinity can be made rigorous in any way. Conversely, one could claim that at each finite position of either sequences is the value is finite. It does not really matter whether one is twice as large as the other.
You did really hard work for this video. Great video!
Very clear explanation surprised by clear visuals. 👍
Please help me, how can I synchronise the animations with the audio? What I am thinking is that I should give long pauses by using `self.wait()` and then trim the video according to the narration. I suppose this is not the best method, please share your method if you have better one.
Yes, this is how I do it as well combined with another method: I cut the animation into pieces and vary the speed of the pieces. I think variations between 50 and 200 percent are easily compatible with a decent performance.
@@Number_Cruncher Thanks a lot for your reply. Can we talk on Discord? My user name is Richie#3399.
I like this better than the proof involving decimal representations.
Thx! Although it is similar in spirit and the diagonalization argument is easier applicable in other contexts.
Nice video buddy. Could you share the code? I am also learning manim. It will be great to see how you achieve this animation.
I will put it into a github-repository and post the link in a short while.
github.com/mathelehrer/manim/blob/master/video_cantor/cantor.py
I appologize in advance. I'm learning python and manim at the same time. Most parts are most likely rather simple minded and could be done in a more skillful way.
@@Number_Cruncher Aha, your code is so nice to analyze. Hope I will learn something new. Could you explain how you add your voice in the video? Currently, I use shortcut to add voice, but it seems very hard to detect the actual frame to merge the voice. What's your strategy? And yes I subs your channel, Cheers.
I use audacity for recording. Afterwards I apply some noise filters and cut out breaks, that are not needed. For merging audio and video I use kdenlive. Usually, I pause, stretch or compress the video to match with the audio. It is quite tedious, unfortunately.
awesome explaination!
Wow