Can someone explain the "rice on a chessboard is infinite" thing?

>>16704859 (OP)
>rice on a chessboard is infinite
Noone has ever said this, you are a massive retard

>>16704859 (OP)
Not infinite but [math]2^{63}[/math] is a very large number.

>>16704859 (OP)
What is there to explain?
There are 2^(n-1) Rice grains on each respective field so
Rice grains on each field:
1 = 1
2 = 2
3 = 4
4 = 8
5 = 16
6 = 32
7 = 64
8 = 128
9 = 256
10 = 512
11 = 1 024
12 = 2 048
13 = 4 096
14 = 8 192
15 = 16 384
16 = 32 768
17 = 65 536
18 = 131 072
19 = 262 144
20 = 524 288
21 = 1 048 576
22 = 2 097 152
23 = 4 194 304
24 = 8 388 608
25 = 16 777 216
26 = 33 554 432
27 = 67 108 864
28 = 134 217 728
29 = 268 435 456
30 = 536 870 912
31 = 1 073 741 824
32 = 2 147 483 648
33 = 4 294 967 296
34 = 8 589 934 592
35 = 17 179 869 184
36 = 34 359 738 368
37 = 68 719 476 736
38 = 137 438 953 472
39 = 274 877 906 944
40 = 549 755 813 888
41 = 1 099 511 627 776
42 = 2 199 023 255 552
43 = 4 398 046 511 104
44 = 8 796 093 022 208
45 = 17 592 186 044 416
46 = 35 184 372 088 832
47 = 70 368 744 177 664
48 = 140 737 488 355 328
49 = 281 474 976 710 656
50 = 562 949 953 421 312
51 = 1 125 899 906 842 624
52 = 2 251 799 813 685 248
53 = 4 503 599 627 370 496
54 = 9 007 199 254 740 992
55 = 18 014 398 509 481 984
56 = 36 028 797 018 963 968
57 = 72 057 594 037 927 936
58 = 144 115 188 075 855 872
59 = 288 230 376 151 711 744
60 = 576 460 752 303 423 488
61 = 1 152 921 504 606 846 976
62 = 2 305 843 009 213 693 952
63 = 4 611 686 018 427 387 904
64 = 9 223 372 036 854 775 808


Total sum = 18 446 744 073 709 551 615
Grains of rice

>>16704875
@claude is this true? it's unbelievable
https://www.youtube.com/watch?v=sfCLt0kTd5E

You can proof it by induction:

show ∑ₖ=1n 2ᵏ-1 = 2n–1 for all n≥1

Base: n=1
∑ₖ=11 2ᵏ-1 = 20 = 1
21–1 = 1

IH: assume ∑ₖ=1n 2ᵏ-1 = 2n–1
Show for n+1:
∑ₖ=1n+1 2ᵏ-1 = (∑ₖ=1n 2ᵏ-1) + 2n
= (2n–1) + 2n by IH
= 2·2n – 1
= 2n+1 – 1
Therefore, by induction, ∑ₖ=1n 2ᵏ-1 = 2n–1 for all n≥1.
Plug in n=64 to get 264–1 = 18,446,744,073,709,551,615

QRD

>>16704882
*2^64-1

>>16704859 (OP)
>rice on a chessboard is infinite
no such thing to explain.

After the 33:th square the rice on the board is already heavier than the world's heaviest tank, Panzer VIII Maus. That's what exponential growth does. It almost looks like it's getting infinite but it's not.

>>16704898
OH NONONO MAUSBROS?

>>16704875
That makes about 535 billion tons of rice. 3590 times how much rice are produced in China in a year.

>>16704898
>>16704909
holy shit science fucking rocks

1.2.4...infinity. science rulz!!1

>>16704898
Illuminati confirmed. Maus'dib has entered the chat.

>>16704859 (OP)
to process incomprehensibly large numbers we almost necessarily need to construct them in a useful manner. 2^64 is enough information to do some pretty cool things, but unlike "six take away three" we can never fathom 9 quintillion items.

>>16704996
1000000000000000000
1000000000000000001
1000000000000000002
1000000000000000003
1000000000000000004
1000000000000000005
1000000000000000006
1000000000000000007
1000000000000000008
9 quadrillion items conveniently displayed as an aid for your comprehension.

>>16704860
>>16704863
>>16704875
>>16704882
Finite chessboard shills out early today.
>>16704898
>>16704909
Real /sci/ bros save the thread.
>>16704996
>>16704998
9 quadrillion.
What a roller coaster ride.

>>16704998
>>16705000
>9 quadrillion
can't tell if this board or /f/ takes the cake as the board with the saddest decline

>>16704909
>>16704898
How much rice is there in the world and how many squares would it take to get there?

>>16705001
Can you demonstrate evidence of better times, preferably in screen cap format?

>>16705001
>The Comma Nazi Haz Arrived!
/thread

>>16705011
With ease and gusto, newfag

>>16705017
any mouthbreathing retard knows 10^18 is a quintillion. you have no excuse.

>>16705001
9 trillion !!!

>>16705020
>Behold, The Grammar Homosexual Has Also Arrived!
We have a contender.

>>16705019
>10^18
Exaillion

>>16705028
> homosexual as a noun
apparently, you and your mother are homosexual

>>16704859 (OP)
>infinite
stopped reading there

>>16704909
Almost certainly more rice than has been harvested in all of human history.

>>16705056
No free refill on rice.
$1.50/bowl. Dine In ONLY.

>>16704917
I love to lurk sci as non math or science bro and learn crazy things like this :3

also what does that weird look E thing mean in this guys post >>16704882

>>16704859 (OP)
>King rewards subject
>greedy subject is greedy
>King imprisons and punishes suspect for their outsized greed
If the man asked for a princely pension he would have recieved it. Instead the man ended up with less than he had before he demanded payment.

>>16705071
>wtf bat signal?!?
Poster is double-twice-pointed-to as "based" and "knows". Can prolly triforce too.

>>16705071
lil bro doesnt know what a sigma is no cap

>>16705071
>>16704917
Get this. By the last square of the checkerboard,
you can fit all 18.4 quintillion grains of milled rice
in about 40,386,961 silos each containing about
500,000 bushels of rice.

If the famous story holds true in this regard,
the king would have to fight the entire world
full of granaries a number of times over
to fulfill the reward of one man, and yet be
61 magnitudes short of all particles of the
universe--completely eclipsed by the mass
of ya moms ;)

>>16705077
The King could have handled this in a variety of clever ways.
All the King had to do was just laugh and say "Oh my you are such a clever fellow! I will certainly honor my promise! But it may take a long time to fully collect your reward. I will pay you ONE GRAIN OF RICE PER YEAR!"
or
"Here is my IOU for all that rice, once you have brought me all the sacks needed to haul it away you shall be paid."
or
"Fine then, on the first day you will receive one grain of rice, on the second day we will split one grain in half, making two grains of rice, then the next day one grain split into quarters to make four grains, and so on until you have been paid in full."

>>16705372
Rather astutely, the kind said that it would be better if instead of 2^64 of rice he would give a board 2^∞.
Of course, 2^∞ = ∞ = (1 + 2 + . . . ) = -1/12
And this is how fractional banking was born.

>>16705000
This is how you spend your limited time existing? Shitposting for attention and trying to spread disharmony amongst people you don't even know?

>>16704859 (OP)
I will try. But I am just an ordinary guy.
Basically its just analogous to demonstrating that every infinity contains an infinite number of infinities. WIth each of those infinties doing the same.
Or "Infinities all the way down" sort of thing. And infinities all the way up. Infinities in all directions, in all dimensions, The ultimate hall of mirrors.
Its open to interpenetration of course, depending on one's own philosophy of math, but some people use it as a way to mock the very concept of infinity. Those who subscribe to the notion just remark its just an interesting observation about the nature of their own particular of mathematics.
I have no particular opinion on the subject. But I do observe that the pure mathematicians tend to favor the former, or at least tolerate it, while the engineer types favor the practical applications and get irate when mocked for their pedantry.

>>16705003
In 2022, the total world rice production was approximately 776 million metric tonnes. The largest producers include China, India, and Indonesia.

>>16705388
The chessboard is clearly non-finite.
One can argue uncountably so.
Integrate, Anon. Integrate.

>>16705428
>every infinity contains an infinite number of infinities. WIth each of those infinties doing the same.
>Or "Infinities all the way down" sort of thing. And infinities all the way up. Infinities in all directions, in all dimensions, The ultimate hall of mirrors.
Dude, thank you.
You just made Banach-Tarski seem completely normal. Over the Naturals, Integers, and Reals it is. It's only on the sphere where things start to get weird and you need AoC.

Let us be perfectly clear. Infinity is an affront to GOD and all that is good and decent. The Universe is finite and granular. There are no infinities, just like there are no unicorns or flying pigs ( unless you count police helicopters ).
Its time for Mankind to come to its senses and purge this Earth of all mention of infinity.
Brothers and Sisters of the ONE TRUE FINITE FAITH, it is time to rise and seize the Holy Land of Mathematics back from those GOD CURSED INFINITY LOVING SODOMITES!
DEUS VULT!

>>16705071
The E means sum.
https://www.mathsisfun.com/algebra/sigma-notation.html

Here's a comparison of the moon (left) and the rice if all the 18446744073709551615 grains of rice were put into a huge ball. It would have a diameter of 10.849 kilometers assuming rice density is 800 kg/m3 and one grain weighs 0.029 grams.

>>16706120
Amen Brother.
But I have one question.
Is immolation too merciful a punishment for the Cantorists?

>>16704898
>After the 33:th square the rice on the board is already heavier than the world's heaviest tank
and after the 34:th square the rice on the board is barely heavier than your mom

>>16704909

that's more rice than stars in the universe

>>16704901
>OH NONONO MAUSBROS?

I BUILT THE TONK! (Frantic)
https://m.youtube.com/watch?v=vl1a8ws-aJo

The Tonk is a basic but still works tank. It has a 76 millimeter Auto Cannon. The Tonk is designed around the comet.

The Tonk has a single track, a double track with a hole in the middle, and no track at all. The Tonk has a hole in the exhaust.

The Tonk has a Commander's cupola. The Commander's cupola is slotted directly on the top in the middle and is thinned down.

The Tonk has a driver's view. The driver's view is directly on the top of the Tonk.

The Tonk has a fuel capacity of 50. The Tonk has a transmission. The Tonk has an engine.

Unironically, The TONK might be a great choice for modern drone vs. tank warfare. As it is lightweight, but armored it can move very fast (limited fuel capacity / limited ammo capacity), is cheaper to manufacture is a one-man vehicle. So field unit loses are about the same, but at a higher cost. Essentially, it's a armored fast grenade, bazooka launcher with limited distance but very fast travel over bad terrain. Ideally you'd have a separate refueler and a separate weapons storage platform which would require a Bluetooth or encrypted chat system to initiate reloads as a imposter would have easy access to blow up the Tonk Army.

Lots of crazy dudes with fast low yield weapons emissions overwhelming genuine slow tanks on a battlefield (attrition by cheapness) meaning a field of 10 genuine tanks vs. 30 Tonks should be like trying to swat skittish flies. Meanwhile you have 30 TONK bazooka yield guns taking potshots and fleeing faster than they can be target locked. A 6 to 8 man crew inside the genuine tanks means an 80 man death toll plus multiple millions of dollars spent. 30 Tonks means maybe 2 million lost for 30 Tonks, and 30 dead Tonk operators.

Tonks wouldn't last against this.
The CBU-105 smart anti-tank bomb in action on trials in the United States.
https://m.youtube.com/watch?v=_cFkEXHBIkk

Infinite is way more than "a lot". If you used every atom in the universe to encode an additional power to raise the total number of atoms in the universe to, you would still be closer to 1 than infinity. In fact you could repeat it for an endless number of universes and you still wouldn't be any closer to infinity because infinity is defined to be above any number that can be conceptualized.
You can never reach infinity because it's qualitatively above not quantitatively.
Throughout history infinity is virtually never invoked in the way we understand it nowadays, they always simply mean something to be endless which is closer to the definition of a limit. The actual infinity is a concept that came much later despite what people think.

>>16704859 (OP)
I think its an undefined number of rices by the 20th chess square

>>16708557
This is exactly the Satan spawned nonsense which has corrupted the minds of otherwise good decent people.
This GOD CURSED BLASPHEMY has no place in mathematics! And all those who think otherwise must be put to the sword.
Say with me BROTHERS and SISTERS of the ONE TRUE FINITE FAITH!
DEUS VULT!
DEUS VULT!
DEUS VULT!
Amen.

>>16705077
Pension is not payment

>>16704859 (OP)
>"rice on a chessboard is infinite" thing?
did chatgpt tell you that?

>>16708632
https://www.youtube.com/watch?v=UIKGV2cTgqA

>>16708557
Yes, infinity isn't a number or object, it's an unending process with the basic metaphor being counting the natural numbers (1...2...3...) This also goes for infinitescimals.

The Fundamental Theorem of Calculus isn't just a mathematical theorem, it describes the fundamental nature of all processes, including time itself. We experience time in two interdependent and mutually necessary perspectives: instantaneous change in the ever-changing flux of a singular experiential moment (Differentiation, the mode of present sense-experience) and cumulative change over time (Integration, the mode of narrative.)

>>16710262
Someone is asking real human beings for input on a question. As opposed to you know, asking a mindless chatbot.

Maybe smug gatekeeping nerds on the internet attacking anyone who dares to ask a curious question is part of the reason why people are driven to chatbots?

>>16710281
>that image
lel, semi-related story:
the one time I asked a (carefully written) question on StackOverflow, the product owner of the API I was asking about responded directly to my question and I check-marked his correct and straightforward answer. Good experience, 5/5

For sure though, the comments on Questions with a lot of visibility/points were insufferable sometimes
Their real downfall in my opinion, is still not allowing Questions to ever be asked again just cause someone already asked a similar thing 12 years ago

>>16710281
>Can someone explain the "purple on a cat is multiplicative" thing?
Neither you nor OP are real human beings.

>>16704909
That sounds weirdly small in comparison. I thought it would be some incomprehensibly large proportion

>>16710281
ask retarded questions, get retarded answers.

>>16704875
Write down all the powers of 2 from 2^1 to 2^64. Then write down a bunch more. Take the reciprocal of all the numbers you wrote. Add them up. Wa la. Your result will be equal to 2.

>>16704875
a gang of rice

>>16711471
Ok I just wrote down all all the powrs of 2 from 2^1 to 2^500 and added the recprocals but I only got [math]1 - 2^{-500}[/math].
Explain this!

>>16710283
good riddance honestly, basically everyone would rather just prompt a chatbot than deal with stack overflow

>>16712321
>Explain this!

>>16711471
>Write down all the powers of 2 from 2^1 to 2^64.
correction: from 2^0
>Your result will be equal to 2.
correction: almost equal

>if you had one grain of rice for each dick OP sucked, you still wouldn't be close to infinite
Yep, infinity is just that huge.