Here is the story of one simple proof, the roots of which go deep into the world of higher mathematics. There are no strict mathematical justifications and formulations in this story, but there is an attempt to introduce an inquisitive viewer towards a mathematical miracle. The story is based on the modest view of an amateur mathematician on a paradoxical result, which has a rigorous proof and which once delighted the author to the depths of his soul, but for many years remained only a result on paper, and I'd really wanted to feel it from the other side.

First let me ask you one question. Surely you know how to add numbers, and you do it well. But how well? Are you sure? My first task today is to make you doubt this. First, I will tell you some funny and not so funny proofs that zero is equal to one. Next, we will add a lot, talk about number series and indefinite forms, come to the conclusion that zero can indeed be equal to one, and also find a greater mathematical truth in this glaring contradiction.

Enjoy watching!

Time codes:
00:00 Content review
00:38 Some proofs of 0=1
02:25 Geometric progression of logarithm of two
04:50 How to conclude 0=1 based on addition
06:21 Preliminary conclusion
07:02 Put arms around the problem
09:40 New interpretation and harmonic series
12:48 Reordering means sum changing!
14:30 Difference of two infinities
18:10 Is sum of geometrical progression wrong?
19:04 Base definitions
19:42 Historical note
20:59 Comment for most curious
21:42 Conclusion

All animations have been created using Python along with #manim (https://www.manim.community/)

#математика #maths #парадокс #paradox #mathtricks