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143 : true
51,983 Views • May 13, 2024 • Click to toggle off description
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For an alternate wide-format wordless geometric series dissection of the same fact, check out
• Geometric series: sum of powers of 1/...
This animation is based on a visual proof by Warren Page from the September 1981 issue of Mathematics Magazine, (page 201 - www.jstor.org/stable/2689632 ).
#manim #math #mathshorts #mathvideo #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #calculus #series #geometricseries #infiniteseries #base2 #binary #zeno #paradox
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Views : 51,983
Genre: Education
License: Standard YouTube License
Uploaded At May 13, 2024 ^^
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RYD date created : 2024-07-08T21:54:22.28826Z
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83 Comments
Top Comments of this video!! :3
These visual representations are gold.
3 |
That make sense and thank you for giving new information about infinite sum❤
24 |
I think you can also use a segment or a cube. If you can imagine it, you can also use a tesseract, etc
4 |
Yes definitely I concur
3 |
this kind of correlates to the achilles and the turtle pradox. achilles gives the turtle a 10 foot headstart but cannot ever reach the turtle because to get to the turtle he would have to travel 5 feet (1/2) but to travel 5 feet he would have to travel 2.5 feet etc etc. basically achilles cannot win the race because MATHEMATICALLY he needs to cross an infinite amount of points to reach the turtle
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so 0.nnnnnnnn... =1 in base n+1? I know that's not the proper notation but you get the point
5 |
instead I can use more space without making any sense of it!
4 |
You’ve basically made this video several times already… 0.XXX… = 1 in any system that’s base-(X+1)
5 |
How can you divide above base 2 in base 2? Wouldn’t it technically be 1/10, 1/1000, 1/10000???
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1/2^10sD
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If I remember correctly ratio test proves this as well
(1/2) / 1-(1/2) = (1/2) x (2/1) = 1
3 |
I have a guess . 1/k + 1/k² + 1/k³ +... = 1/(k-1). Is that true?
1 |
Suddenly computer science
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Okay yes, on its surface, this is trivial enough to understand. But what does INFINITY really mean in that context?! You start with measurable Quantities (numbers) and you extend the limit to an immeasurable Quality (i.e. Infinity)! We are mixing mathematical spaces here. This is as crazy as saying that the infinite sum goes from k=1 to Aleph null.
4 |
There will always be a small portion not shaded because you are not filling in a full square each time. You get closer and closer but never reach a full square.
7 |
👍
3 |
🥰
2 |
nigerundayo!!
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And you actually believe that? You are stuck in Zeno's Paradox and can't extricate yourself.
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@Living_Murphys_Law
6 months ago
In theory, could you do a similar argument to prove 0.99999999...=1?
129 |