More Math :3

If we used a base 12 counting system, this wouldn't work btw. .9 repeating will never actually equal 1. It's just due to how we use numbers.

Same works in Base12 actually! Just not with the digit 9. If we use: 0 1 2 3 4 5 6 7 8 9 A B, Then 0.BBB... = 1

So I just went into a deep dive on this and it turns out i believed in hyperreal numbers without knowing what they were. Cool.

Ngl an easier way to show anyone not too versed in algebra is by showing them the pattern for any number divided by 9. Starting with 1⁄9, you get 0.1̅, arriving to 8⁄9, you get 0.8̅, & following that pattern, you'd expect 9⁄9 to be 0.9̅, & 9⁄9 is a whole fraction, so 0.9̅ = 1

Didn't know VR chat furries teaching me math in a winter cabin over a fireplace was a genera of entertainment I needed.

0.999x10=9.99 not 9.999 also you resolving x in the second cell but you are not resolving x in the first cell, you just assume t hat x is x [because x can't be two values, yes but you separated it] if you remove decimal you must add x-decimal to complete the equation. aka 0.999

That's actually incorrect. 0.9̅ × 10 is still equal to 9.9̅ with the decimal. This is because the decimal repeats infinitely. 0.9̅ is just another way to write 0.99999.... (infinite nines) So when we shift the decimal place by one, we still have an infinite amount of nines.

i think you are incorrect and lacking of understanding how important a fraction of something is sorry, we cannot just make up math, i don't know what teachers teaching you in school nowadays but you cannot generalize in math e.g. pi ellipsis means you just don't represent it

Official documentation of this by the way. Here's a Harvard paper explaining the same concept. We're not "making up math". This is the standard.

well math states x=/=xε unless ε=0

@Wrenosaur_ I found it helpful to view it as a geometric series. 0.9(0.1)^0 + 0.9(0.1)^1 + 0.9(0.1)^2 + … + 0.9(0.1)^n = 0.9(1 - (0.1)^n)/(1 - 0.1) = 1 - (0.1)^n As n -> inf, 1 - (0.1)^n -> 1

@HanRongYao Yes! You can actually express it as this

By that logic any number is equal to every other number (20-X = 19) and a separate equation (25-X = 19) uses the same logic that would prove that and 6 and 1 are the same number The X value AND the starting value WEREN'T the same in the video, which doesn't prove squat

20 - X = 19. X = 1 25 - X = 19 X = 6 No, it doesn't create equivalence between any two numbers. It simply states that (0.999...) = 1.

Nope. The X wasn't the same number in YOUR logic, and you can only prove it with the assumption that 0.999 is 1, which is what the problem is trying to solve. It's a simple case of circular reasoning. You can only prove it with the assumption that its already true,

If we consider that x = 0.999... Then we can prove that 9x = 9 That means that x = 1. The equivalence is gathered through transitivity. 0.999... = x = 1 0.999... = 1 You can prove this very neatly through summations and limits as well. The sum converges infinitely.

Then how come the proof is in the red but you can only find the proof by assuming the proof is real in the yellow before you find the answer in the red

We didn't assume anything. This was gathered both in the video, and in my comments to you. If you claim that my explanation is wrong, then please point out exactly where this mathematical proof fails.

Here because you're assuming they're the same and not slightly different by an infinite margin because its a infinite ending in 0 and not an infinite ending in 9

"Infinite ending"... 😐 The definition of "infinite" is never-ending. Infinite has no 'end'. What are you talking about?

Bro got a tongue so big it is distracting

Yoooo

I love math. And it felt good to finally learn a new math concept. It’s been years! :3

You genuinely left me stunned. No error in the math, no errors in your explanation. Dang.... (I'm really a math nerd, and I really don't do this XD)

The weird math-logic way of explaining this property is that 1.0 and 0.999 have no discernible, finite values between them. You can always find another number between any two numbers on the number line. If you cannot find a value between two values, then they’re the same number.

This is a good intro to get people to start understanding limits, but it ultimately fails since 10x-x is arbitrarily 9x in this system. A better way to prove this is with the Archimedean property, or even the nested intervals theorem (idk if most people will understand that tho)

I was just gonna say rounding

Bro where were you when I was in high school

Another easier way to approach this problem, and my personal favorite, is with fractions: 1/3 = 0.333... 0.333... × 3 = 0.999... 1/3 × 3 = 3/3 = 1 0.999... = 1

great! now, divide by zero and make it work

I was completely unaware that if I wanted to learn math, I needed it to be taught by a furry femboy in vr chat. The More You Know🌈

Great vid

So I kinda have a question: Mainly, can we actually assign a variable to an infinitely repeating number like that and have it behave like a normal number? I can't help but feel like assigning a variable would have to mean that there'd need to be a definite number of 9's

There's plenty of instances in math where we assign variables to infinite expansions & series. It actually helps us find solutions for these problems. Also, we dont have to assign a variable to 0.999 for this to work. We can write it out without saying x (it's just inefficient)

(0.999...) + (0.999...) +(0.999...) +(0.999...) +(0.999...) +(0.999...) +(0.999...) +(0.999...) +(0.999...) +(0.999...) = 9.999.... That's ten 0.999...s, So, 10 × (0.999...) = (9.999...) 10 × (0.999...) = (9 + 0.999...) (minus 0.999... from both sides) 9 × (0.999...) = 9

Furry math is the best:3

I can't remember the last time the transitive property was relevant, much less to resolve an apparent contradiction...but this looks like it checks out. o.o

If you torture numbers enough, it will confess to anything.

I pray for a day that a math teacher pulls out video like this

My god how far I would excel in math if all my math professors were this cute

The end blooper is so relatable 😂😂😂

w pull

i learn something new everyday.

This fucking guy is better than my math teacher😭

Holy shit

A lot of people who have never taken a college math class getting real confident in the replies. Especially the people claiming that you're wrong because they think 10*0.999... would actually be 9.99 not 9.999 without realizing that it's infinite decimals.

Please teach me curvature and torsion

Please more math!

10x0,999=9,99 so 9x=9,99-0,999 which is equal to 8,991 so this is really fucking incorrect

It's correct. It's an infinite decimal. Its not just 0.999 hard stop. It's 0.9̅9̅9̅. It repeats forever. 0.999999999..... (infinite nines)