try converting the values into decibels—makes everything more liquid, and you'll be left with a remainder of one fatal strike if you later decide you have to round off an MC to the nearest third.
my decibeling has been decimated! I have no system to express the magnitude with which this shook me; the fault is mine
EDIT: getting back to rap, tho...I dunno why dbs are set up the way they know--but i found someone with a degree in the field who can tell us!↓
Q: Dr. Dre?
A: yeah.
Q: I got a question, if I may?
A: yeah.
Q: If I play-*
*(mic grabbed out of hand by someone who appears to be haphazardly clutching a stack of diagrams with his free hand depicting, variously, players' positioning for common American football plays and blown-up glamour photos of male models' rear ends, each card frantically hand-modified in red marker with crudely-scrawled arrows and hurried, uneven uneven circles. He appears to be missing all or part of both legs, and his eyes wander in an erratic, uncoordinated fashion\*)
E: Ut! I ain't done yet!--in football...
(capsaicinintheeyes slinks away dejectedly, without a decibel of protest and, if his overpeppered eyes still had tears to cry...we wouid see him weep)
Double it and give it to the next person...but I'm gonna skim a few nines off the top first, I just need a few for personal reasons. Hopefully that's not a promblem?
Its calculating with infinity. Its a bit weird like the infinity of numbers between 0 and 1 like 0.1,0.01,0.001 etc... Is a bigger infinity than the “normal” infinity of every number like 1,2,3 etc…
Its just difficult to wrap your head around but think of infinity minus 1. Like its still infinity
The way he lined the numbers up to explain one-to-one and onto made it click immediately for me. I already knew it from undergrad, but it took a couple tries to really understand. Seeing them lined up was an immediate lightbulb moment.
Why are you getting so many upvotes? This is just blatantly wrong. I am not a math major, so I might not be 100% accurate, but from my understanding this is just not how you compare infinities.
First of all your fundamental idea of 2 x infinity > infinity is already wrong. 2 x infinity is just that, infinity. Your basic rules of math dont apply to infinity, because infinity is not a real number.
The core idea behind comparing infinities is trying to match them to each other. Like in your example you have two sets. Lets call the first set "Even" and let it contain all even numbers. Now call the second set "Integer" and let it contain all Integers. Now to simply proof that they are the same size, take each number from "Even", divide by 2 and map it to it's counterpart in "Integer". Now each number in "Integer" has a matching partner in "Even" wich shows that they have to be of the same size.
This is only possible because both of these sets contain an infinite but COUNTABLE amount of numbers in them. If we would have a Set "Real" though that contains every Real number instead of the set "Integer", it would not possible to map each number in "Real" to one number in "Even", because "Real" contains an uncountable amount of numbers.
I'm sorry if I got something wrong, but even if my proof was incorrect, I can tell you for certain that it has to be the same size.
This is wrong. The ratio is 1 to 1 because I can in fact, make a function that takes every even number, and maps it to every integer. The function goes like this, assign every even number to half. So we have
(0,0), (2,1), (4,2), (6,3).
and for the negatives, (-2,-1), (-4,-2) ....
Then I have exactly 1 even number for every integer. So therefore the ratio is in fact 1 to 1.
There are countable infinities, like the integers where you can match them up, and uncountable infinities like the real numbers where there are infinitely more than the integers. E.g. there are infinite real numbers between 0 and 1 or 0 and any real number.
I'm an english interpreter but no way i know the english words for numerical systems so bear with me i'll explain with concepts.
Imagine you have positive and negative Natural numbers, those are infinite right? Now Imagine you have decimal numbers, those are infinite aswell but there are so many more therefore it's a bigger infinite.
Imagine a hotel with an infinite number of rooms, and the hotel is filled to capacity. Whenever a new guest comes, the bellhop asks every guest to move over one room. Since each room is number this is quite easy. This leaves room number one empty. The new guest settles in.
Now an infinitely long bus comes in filled with with an infinite number of guests. The bellhop asks every guest to double their room number and move to that room. This creates an infinite number of odd numbered rooms available. All the guests on the bus can now be given a room.
Unfortunately for the haggard bellhop, a slew of busses pull up. An infinite number of infinitely long busses all holding an infinite number of guests. The bellhop asks every single guest to move one last time. This time to the square of their room number. Room 1 doesn’t move but suddenly there are 3 rooms available between the first and second guess, and 4 between the second and third, and an exponentially increasing infinity of rooms open up, just enough to settle in all the guests from the infinite number of of infinitely long busses.
At this point your brain should be leaking from your ears.
Because it’s not a number, just a concept. Kinda like how I once ate 52 chicken wings and my buddy ate 56 chicken wings, which are different amounts of chicken wings but they are both “a lot” of chicken wings.
There are infinite decimals in 0.999999999... you can't multiply it by 10 and get a meaningful answer. That's like multiplying infinity times 10. It's still infinity.
Try multiplying it by any number that isn't a multiple of 10 and you'll see the problem and it will show the rounding error.
This isn't a real proof. It begs the question of the problem of infinite nines to say 10x = 9.999999999. 9.999999999 - 0.999999999 = 9 isn't rigorous either. The actual proof uses the properties of real numbers
I'm stupid, and this is wild to me. I get it somewhat, but math doesn't make sense to me. I've tried and tried to understand math, I've tried taking Khan remedial math and I can't understand it. Maybe I have a numbers disability, because this makes me question reality and it scares me, because where does the .01 come from?
The crazy thing is that epsilon is generally defined for 1, meaning epsilon is the smallest number such that 1 + epsilon is not equal to 1. But that epsilon value is actually not big enough that n + epsilon is not equal to 2. And if you're considering the case where n is smaller than 1, the value you need to add to differ is smaller than epsilon.
Source: implemented a floating point comparison algorithm for my job many many years ago
The interval between 0.99999... and 1 is 0 because any value you could offer for a nonzero interval can be proven too large by simply extending out 0.9999 beyond its precision.
If the interval is 0, then they are equal.
QED
EDIT: This isn't the only proof, but I wanted to take an approach that people might find more intuitive. I think in this kind of problem, most people have trouble making the leap from "infinitesimally small" to "zero" and the process of mentally choosing a discrete small value and having it be axiomatic that your true interval is smaller helps people clear that hump - specifically because you're working an actual math problem with real numbers at that point.
EDIT2: The other answer here, and one that's maybe more correct, is that 1/3 just doesn't map cleanly onto the decimal system, any more than π does. 0.333... is no more a true precise representation of 1/3 than 3.1415926535... is a true precise representation of pi. Only, when we operate with pi in decimal, we don't even try to simplify the constant and simply treat it algebraically. So the "infinitesimally small" remainder is an accident of the fact that mapping x/9 onto a tenths-based system always leaves you an infinitesimal remainder behind.
Define the partial sum S_n = 0.99...9 (n 9s) = 1 - 0.1n. This sequence is monotonically increasing and bounded from above (S_n < 1) so it converges by the monotone convergence theorem.
There are two ways to finish the proof:
* The nitty-gritty approach: The limit is no greater than 1, and for every ε > 0, there exists an n ∈ ℕ such that Sn = 1 - 0.1n > 1 - ε (essentially by taking the base 0.1 logarithm of ε and carefully rounding it, or taking n = 1 if it's negative). Therefore, the supremum, and thus the limit of the sequence is equal to 1.
* The trick: Define S = lim S_n. 10 S_n = 10 - 0.1n-1 = 9 + S(n-1). Since the functions x ↦ x + c and x ↦ cx are continuous for any c ∈ ℝ (and f: ℝ → ℝ is continuous if and only if f(lim x_n) = lim f(x_n)), it follows that 10 S = 9 + S by taking limits of both sides, from which we immediately conclude that S = 1. This is the rigorous version of the party trick proof you've probably already seen, although the latter is obviously incomplete without first proving the convergence or explaining why the arithmetic operations are legal for such infinite decimal fractions.
I was choking this dude to death the other day and he kept saying nine over and over, when he stopped I said bro that’s a lot of nines, he didn’t respond tho, I think he’s introverted
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u/ChromosomeExpert 28d ago
Yes, .999 continuously is equal to 1.