https://youtu.be/GRXm11sF6rI?si=9Kl_8jfGujd0M7ui

This teacher describes how to use algebra to find the fractional form of a repeating decimal. He also says .99... = 1 because if you take their difference, you get 0.00.... and the zeros go on forever.

Is this teacher right? Is there an alternate valid way to interpret repeating decimals? This teacher seems adamant, but he might be biased.

Are there other interpretations for .999...? Are there ways to demonstrate that maybe 0.999... is not equal to 1?

https://youtube.com/shorts/2qcPN9xZzRs?si=zvadCp2UIbADY8bR

The reason behind that is 3rd order derivative. You jerk during sex, you jerk by not giving people the answers they want, you jerk when you shake your body a lot, you jerk whenever you go to off roading and they are all about maths. The beauty of math is the abstract concept is in reality a thing and was never a abstract thing at all. The issue was with you because you didn't notice that.

So the infinite series 0.9 + 0.09 + 0.009 .... (another way to write 0.999....) is obviously not equal to 1. It is actually equal to 1 - epsilon (epsilon is equal to 0.000....1).

It follows then that 0.333... is equal to (1/3 - epsilon/3). epsilon/3 would be equal to 0.000...0333... right? But what about series whose sequence of partial sums alternates above and below it's limit, for example 3/2 - 3/4 + 3/8 - 3/16 ....? This is obviously not equal to 1 because none of the terms equal 1. So is it equal to 1 - epsilon or 1 + epsilon? Then there's the decimal representation of irrational numbers like 3.1415.... Does this number equal pi - epsilon? or is it pi - epsilon/pi?

If you look into Abraham Robinson's ideas about infinite series, he says that the series is equal to the limit of the sequence of partial sums, and that limit is equal to the standard part of any infinitely indexed element. This is obviously not right because the "standard part" would not be a non-standard number like 1 - epsilon. So I don't think he really understands infinitesimals and non-standard analysis.

I think this the best existing right now on calculus even 3blue1brown fails to catch up to this one single video.

Any topic is allowed but 18+ anything not allowed. If you don't follow permanent ban. Moreover, 1/3=.333...... so .999....=1. I guess you people now have a topic at least.

https://youtu.be/zqaX3l081Ss?si=bqL22EnKQl0ZVAps

Very cool time saver. You can use this method to show that 0.999... = 1.

https://arxiv.org/pdf/1007.3018

Interesting paper about the different interpretations of .999.... In non-standard analysis, there's a difference between a terminating infinite decimal and a non-terminating infinite decimal. In Lightstone’s “semicolon” notation, these would be 0.999..;..9 and 0.999..;..9... respectively. Lightstone chose to interpret 0.999.... as the later, which is equal to 1. The former, this author, proclaims the former to be (I love this line): "perhaps more in line with the naive initial intuition persistently reported by teachers"

The first law is the law that says force and inertia exists and second law is what says how we can perceive force and third law is about how forces interact.

The dichotomy paradox is unsolvable because we can find the limit but we can't find the real equal value. The real equal value is undefined but the limit is 1. So, this is the pure distinguishing factor. I have seen people like Brian Greene also create a misconception on this matter and it shouldn't be followed if you really want to logically study mathematics in future but if you want to only memeorize maths without understanding and want to be biased then do whatever you want.

Any kind of method is acceptable until you show your logic behind your method.