Відео

Me llamo es Arturo 👹

Except they don't, or we automatically have free energy in closed systems. These aren't proofs, they are sophistry.

The duplicates are far from being a quirk of decimal expansion. In fact, _any_ representation of the real numbers by infinite strings over a finite alphabet that can be used to compute computable functions _must_ have multiple representations of some numbers. If it didn't, either some real numbers are unrepresentable and so it's not really a representation at all, or functions that should be computable can't be computed using that representation. "Computable" means "computable by a halting algorithm" for a function whose result is finite; when the output may be infinitely large, such as an infinite decimal expansion, we mean instead "computable by a productive algorithm", where "productive" means _the next character of the output_ can be computed by a halting algorithm. Since reading the input takes time, this implies that each digit of the result depends on a finite amount of the input. Therefore for real numbers the functions that are computable in this sense are precisely the uniformly continuous ones. A representation maps each finite prefix to an interval. For the representation to be complete and unique, the interval can't be open (because it would leave out the end points), nor closed (because the intervals would overlap in at least one point, so representations wouldn't be unique). But if they are half-open (as those who deny that 0.99.. = 1 believe), some uniformly continuous functions become uncomputable, because when approaching the open end of an interval, a finite amount of input can get you arbitrarily close to the boundary but cannot give you the boundary point itself.

wrong. saying 0.999 equals 1, is like saying 1=2 idiot

Now try paying 99% of your taxes.

0.999… isnt a real number and thus equality isn’t possible and you can’t simply preform algebra with it, you can look at it as an infinite equation and say it approaches one which is true but it just isn’t a number so it isn’t one.

The first two attempts are just trash and nobody should accept them.

The hyperreal numbers one is so silly, like it’s just mathematicians declaring “if you believe this, you’re breaking the rules, and the number you believe in is 0”

The best part is that there's an entire video about proofs that 1 = 1

My grandparents had an old barometer with a mercury thermometer built in that was in Reaumur. It drove me nuts because it was so hard to compare to Celsius. I wonder what became of it after the death of my grandparents...

I think the main issue is the assumption that 1/3 = 0.33333... The imperfection of decimal system just does not allows to place the equals sign between these two numbers.

It's ironic how the first and last proof are basically the same but with about 15~ years of studying between them.

Reading people arguing about this is giving me brain damage

0.9r ≠ 1 0.9r < 1 or 0.9r ≈ 1 All Good?

stupid, this is just circle arguments, using infinity to prove that infinity exists.

10:43 Portal in a portal is weird

0:06 LEGEND OF ZELDA MENTIONED

I find it funny ( in a good way ) that the most " understood " and " intuitive " proof of 0.999... = 1 is the Calculus method ( Summation ) 😆

You lost me after the first one

The way i explained it to a kid who asked (whom i babysit) was that 1-0.9999... equals 0.000000...1, which is basically 0. Prob not the best proof, but he's only 7 so doesn't rlly understand fractions yet

Using plancks, the entire Universe is not large enough to write out the digits. Thats crazy.

accept the idea or keep writing the number 9 till the end of time

for the 5th method, i question that interval. why not choosing an x strictly inferior to 1, and superior or equal to 0.9[n]. considering beforehand 1 as within the range is a mere confirmation bias

as i said, if 0.999999... = 1, then 0 = 1 = +∞ also, if 0.99999999... = 1, then 1/0 has a solution within R

The unit symbol is not lower case (it is on IUPAP documents) this would cause confusion with the multiplier kilo. It is only lowercase if you use the NAME of the unit because it is not a proper name.

I'm a simple polish man: I see ,,-ski" surname - I click

This just proves infinities are paradoxes and can’t theoretically exist

Repeating 9 is repeating 1 off from 1

Every time you put a "9" in the number, you make the difference 10 times smaller. If there are infinite nines, the difference tends to be infinitly small, so it simply doesn't exist.

1/inf - 1=0.r9. And if there are no numbers between 0.r9 and 1 well then that “breaks math”

Man this guy's stupid is he sayong that 0.3333... is 4??!! Joke

11:13 is senseless. How can something have infinite surface area but finite volume. And don't reply to this comment stating that the trumpet is defined that way.....just don't

for the first proof i never rlly understood it since what if 1/3 was based off 3/9? and rather than 1/3 = 0.333..., 0.333... = 1/3?? what im trying to say is that the result of 1/3 mightve been based off the assumed result for 3/9 and imo might not prove anything 😭i could be very wrong but thats just my thoughts

1:34. This paradox only works when both the Cheetah and Snail are considered as point masses. In real life, this paradox fails because both Cheetah anf snail are not points but have some length. The cheetah just has to reach a point where the diastance between it and snail is leass than or equal to the snail's body length.

I think 1 - 0.(9)= 1/10_in_power_of_infinity

Actually even in hyperreal, 0.999…=1 can be true. Let 0.999…;…9990 = *0.999… and 0.999…;…999… = 0.999… 1 - *0.999… = epsilon 1 - 0.099… = 0 I read book about hyperreal analysis but it was so hard to understand.

Ok but is 1.999.... equal to 2

if we can "prove" that .999 = 1, we need a new word for these "proofs" lmao. nothing is being proven if we can use the method to come to incorrect conclusions

.999... truthers are given far too much attention 😭

5:00 that's kind of the approach I used in middle school, just that I didn't know how to formulate it properly. In plain language: 1 - 0.9 = 0.1 1 - 0.99 = 0.01 Each further 9 in the sum on the left adds one more decimal 0 on the right. Therefore, the difference between 1 and an infinitely repeating .999... also has an infinite number of decimal 0 positions until we finally get to the 1: 0.00000... (repeat infinitely) ...1 If we were to read this number for any processing purposes, we would never reach the "1" at the end. It's just an infinite string of 0s. The 1 no longer has any meaning.

how much of this video is AI-generated? the voice, surely? what about the script? don't take this the wrong way, but it's ringing some alarms in my head..

i was expecting a simpler version of the LAST explanation to be the FIRST one LOL i.e. "what number would you add to 0.999... to equal 1?"

5:26 scp

What do you think about S1 = 0.9 = 1 - 0.1 = 1 - 10^-1?

HUH

1:33 neat but with all prime numbers being odd adding 2 together regardless would be factors for even numbers

0.99999...989983982≠1 ^^up there is 3t nines

Interesting. I only knew of three of those before. I am trying to comprehend having higher numbers indicating colder temperature. That would be tricky to get used to.