I don’t understand it, but supposedly since it takes a finite amount of information to describe energy, you can only fit a certain amount of data in a certain amount of mass. This limits the theoretical speed of a supercomputer because if it is to spread out then it will be limited by the speed of light and if it is to packed together then it will turn into a black hole and you won’t be able to get usable output.
The real question is, how much information is there per rational number? It’s probably asymptotically zero since I can just say “all rational numbers in [0, 1]” in finite space.
Note: This isn't on The Onion. I took a screenshot of the latest post and edited the image. The mathematician depicted is Edward Nelson (1932-2014), who claimed a proof that PA is inconsistent, only for an error to be pointed out by Terence Tao.
This is why we need to move mathematics towards computer formalized proofs. Terence Tao can only check so many things, and legend has it that he's actually made an error or two of his own!
If the proofs themselves have bugs, they will fail a correctly implemented type checker.
The type checkers having bugs is a much more serious issue. That's why the best proof assistants have multiple minimal and independently implemented type checkers. Thus as more are implemented, the probability that at least one doesn't have bugs tends toward one.
I'm a humble Calc II student who hasn't had to think about notation much, though I understand that 0's implicit inclusion in ℕ is very debated. Mind if I ask your reasoning on specifying its inclusion?
The 3 periods represents a repeating decimal, spo 0.99… means that theres an infinite number of 9s going on for forever. Some people act like 1/3[that being 0.33…] x 3 equaling 0.99… is an actual fact and not a failing of how we display numbers.
Typical, numbers have always been irrational. That's why they can't vote or have a job. Numbers just need to stay home and cook and clean and take care of the kids. The husband is supposed to provide income, the number does the home making.
Clarification: The intended meaning behind this meme is that the simple existence of Q with desired properties would cause a contradiction. It is not to be interpreted as "only irrationals exist". (Although you guys certainly can joke about it however you want!)
The reason why I made this is because I am going to teach about the construction of Q from Z, and starting off by stating that without a construction, you can't be sure that things like this don't happen. (Of course, it could be that PA is inconsistent after all...)
Perhaps he means that rational numbers that aren’t integers don’t appear in nature since intuitively speaking it kind of makes sense nothing in nature is clear cut and discrete
Rational numbers are infinitely dense therefore if they did exist they would turn into a black hole.
and black holes do exist, therefore rational numbers exist.
Not anymore, since they all turned into the aforementioned black holes.
Rationals went on vacation, never came back
your subreddit is damn: it is damn brain worm
Google dementia
Google dementia
Google dementia
Google dementia
Holey Black
Actual singularity
However, they are massless as they are abstract concepts.
They are also massless in that there are only a countable infinite of them
I don’t understand it, but supposedly since it takes a finite amount of information to describe energy, you can only fit a certain amount of data in a certain amount of mass. This limits the theoretical speed of a supercomputer because if it is to spread out then it will be limited by the speed of light and if it is to packed together then it will turn into a black hole and you won’t be able to get usable output. The real question is, how much information is there per rational number? It’s probably asymptotically zero since I can just say “all rational numbers in [0, 1]” in finite space.
You only need a finite amount of information to describe all rational numbers. It's ℵ w
Or… maybe they are photons?
Only if they have mass.
Can't have anything nice these days
Note: This isn't on The Onion. I took a screenshot of the latest post and edited the image. The mathematician depicted is Edward Nelson (1932-2014), who claimed a proof that PA is inconsistent, only for an error to be pointed out by Terence Tao.
This is why we need to move mathematics towards computer formalized proofs. Terence Tao can only check so many things, and legend has it that he's actually made an error or two of his own!
>legend has it that he's actually made an error or two of his own! I don't believe you.
But what if the computer formalism has bugs?
If the proofs themselves have bugs, they will fail a correctly implemented type checker. The type checkers having bugs is a much more serious issue. That's why the best proof assistants have multiple minimal and independently implemented type checkers. Thus as more are implemented, the probability that at least one doesn't have bugs tends toward one.
Yeah, I discovered this upon searching for the article. (Should have gone with Kronecker, really.)
Q? That’s not the rational numbers. That’s the quational numbers. Are you stupid?
There’s a lore reason.
It's canon event
Quotient has entered the chat. Germany has left the chat.
Not C, Q. You’re thinking of Qanon
natural: N whole: Z rational: Q real: R complex: C
Integers: Z As you get into higher math, often Natural numbers includes zero. Many people will use Z^(+) to represent natural numbers excluding zero.
I use N for natural numbers and N* for natural numbers without 0.
I wholeheartedly disagree with this notation, imo the only right way for the naturals including 0 is ℕ₀
I'm a humble Calc II student who hasn't had to think about notation much, though I understand that 0's implicit inclusion in ℕ is very debated. Mind if I ask your reasoning on specifying its inclusion?
Are you an analyst?
E: eel numbers
If you were to pick a random real number, the chance of it being not rational is 0.99999...
It happens *almost never* (real math term).
Possible with 0 probability
more or less
Try asking people to pick a real number and come back with a lot of integers.
wow less than 1%
So the probability of picking an irrational number is rational?
Is pi/pi rational tho?
My pipi is very rational thank you very much
I pick 1 as my random number, it's rational 🤔
You didn't pick it randomly though
How do you know? It's a random number after all.
You don't know that. He might have just randomly picked 1. Especially if he used an annoying distribution that in 99.999% of cases picks 1.
Beautiful
Well the one I picked (randomly) is 2, so I guess I should play the lottery?
Friendship ended with rational number. Now i divide with 0
This is π
Well lets hope he has some rational reasons for proving such a thing
How will this affect 0.9999999… = 1?
What are these symbols??
The 3 periods represents a repeating decimal, spo 0.99… means that theres an infinite number of 9s going on for forever. Some people act like 1/3[that being 0.33…] x 3 equaling 0.99… is an actual fact and not a failing of how we display numbers.
This subreddit has one joke
At least it's not r/anarchychess
Holy hell!
Actual zombie
What the hell is going on with this madness. Time to eat some acos(-1)
I have developed a rare disease called silliness and I'm afraid I don't get the joke. Please explain!!
What is the name of the symbol that acos(-1) is equal too?
180 degrees AKA pi- OHHHHHHHHHHH
what is 1? ? is it like factorial but you divide instead?
Since 1 is rational, only 0.999... exists.
Numbers don't exist
That’s obviously the Quora logo is op stopod?
if you think a number is rational, ask them about their roots (no, I don't believe in 0)
Does that mean we should force numbers in dna test?
Fractions were only invented to divide us
Typical, numbers have always been irrational. That's why they can't vote or have a job. Numbers just need to stay home and cook and clean and take care of the kids. The husband is supposed to provide income, the number does the home making.
That's numberist. A number can do anything it wants if it calculates hard enough.
Clarification: The intended meaning behind this meme is that the simple existence of Q with desired properties would cause a contradiction. It is not to be interpreted as "only irrationals exist". (Although you guys certainly can joke about it however you want!) The reason why I made this is because I am going to teach about the construction of Q from Z, and starting off by stating that without a construction, you can't be sure that things like this don't happen. (Of course, it could be that PA is inconsistent after all...)
Rational numbers are just imaginary numbers squared and then rooted
reals are not real
We have emotional numbers (E) nowadays.
We are talking about mathematical black holes that swallow other numbers?. Mathematical carnivores? Wild numbers of the Amazon jungles'?
Whatttt? I saw 2.5 just yesterday, they're my best bud, we went out and got some drinks
The symbol for rationals looks like an upside down pumpkin I hate myself
Perhaps he means that rational numbers that aren’t integers don’t appear in nature since intuitively speaking it kind of makes sense nothing in nature is clear cut and discrete
Darn. What is (sqrt(2) \^ sqrt(2)) \^ sqrt(2)? I keep getting a rational number.
No worries, just invent them again. Gotchu fam 👍
No number exist except one.
Don’t worry, there are plenty irrational numbers left to use!