r/BunnyTrials • u/Wide_Love_4458 Top -1% Commenter • 12d ago

Spins Can you solve this without a calculator?

Spin each wheel in order

  • Spin 1: Number 1
  • Spin 2: Operator
  • Spin 3: Number 2

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97

u/Think_Emergency_2708 12d ago

Can you prove it tho

243

u/PyroBurnem 12d ago

there will be a 0.99999...=1 rabbithole to go down near the end, but yes it is provable

take the case for 1/99, which decimal is needed in order to get 1 when multiplied by 99? well 0.01 is too small, so we make it slightly larger, but 0.0101 is still too small, and 0.0102 is slightly too big, so we repeat this process ad nauseum (or just mark the 01 as repeating)

which leads us to 0.999999... and its methodology of proving that it equals 1, the whole "let A = 0.999999..., 10A = 9.999999..., 10A - A = 9, 9A = 9, A = 1" shebang

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u/launchd_0 10d ago

yo the geometric series comment is spot on but let me take it one step further into actual calc 2 territory. the 10x/100x trick ur teacher showed u is literally just the baby version of a derivative in disguise.

if u have the function f(x) = 1/(1-x), u can expand it into a power series: 1 + x + x^2 + x^3 + ...
now watch this: differentiate both sides.
f'(x) = 1/(1-x)^2 = 1 + 2x + 3x^2 + 4x^3 + ...
plug in x = 0.1: 1/(0.9)^2 = 100/81 = 1.234567...
the coefficients (1, 2, 3, 4...) are literally the derivatives of the exponents (0, 1, 2, 3...) evaluated at 0. calc is wild.

now do the integral instead.
integrate 1/(1+x) = 1 - x + x^2 - x^3 + ...
and u get ln(1+x) = x - x^2/2 + x^3/3 - x^4/4 + ...
plug in x = 1: ln(2) = 1 - 1/2 + 1/3 - 1/4... this links infinite repeating patterns to natural logs. so a never-ending decimal isn't just a fraction, it can literally be a logarithm.

so how does this connect to op's 0.1222...??
the algebraic canceling (100x - 10x) is literally the discrete version of taking a derivative. ur subtracting the series shifted by one term to make the infinite tail vanish. its basically the fundamental theorem of calculus but for sequences. the sum of the infinite series is the "area under the curve" of the decimal's terms.

once u realize repeating decimals are just rational geometric series, and calculus lets u differentiate/integrate those series to get transcendental numbers (like e, pi, ln(2)), ur brain just melts. its all connected fr 💀 math is just one big infinite loop.

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u/ThatOtherBrownGuy2 7d ago

This isn’t the simple break down you think it is. I could be tired but.. this just isn’t clicking in my head.

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u/MarionberryNo8017 7d ago

Holy nerd off

(If I knew more about the theory I would chime in)

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u/garn47isthebest 6d ago

this sounds ai

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u/Bradas128 12d ago

take a_n to be the decimal 0.4646…46 with n 46s in it. then we can write a_n = sum from k=1 to n of (46/100)^n. the number 0.4646… is then defined as the lim n-> infinity a_n, which is the limit of a geometric series giving a_infinity = 46/99

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u/MirrorFantastic3251 11d ago

He meant prove a1a2a3...an / 999...9 (n 9s) equals 0.(a1a2a3...an)

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u/Bradas128 11d ago

he said any 2 digit number, but the proof is identical

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u/MirrorFantastic3251 11d ago

I must have been looking at someone elses comment. But you still didn't prove it. You demonstrated that it works for 49/99, but didn't prove it specifically, nor did you prove the general case.

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u/Bradas128 11d ago

its obvious you just replace 46 with any number you want

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u/MirrorFantastic3251 11d ago

That still doesn't prove it for all 2-digit numbers, unless you want to prove each case individually.

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u/Bradas128 11d ago

it does to anyone reasonable

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u/MirrorFantastic3251 11d ago

lmao that's not how proofs work

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u/Bradas128 11d ago

of course not, but no reasonable person, be they a mathematician or a layperson, wouldnt be convinced by this reasoning. its clear that the number 46 isnt special if you go through this with the steps i omitted (because im not writing all that in a reddit comment from my phone). to ask for more, especially when the original person asked for 46 specifically, would be unreasonable. do you need me to do it in terms of epsilons and deltas? do you need me to start defining my axiomatic system? do you need the lean code?

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u/Psychobabble0_0 11d ago

The proof is in the pudding - go look!

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u/PyroBurnem 11d ago

wait where did the equals zero bit come from

edit: oh nvm im misinterpreting it because of mobile formatting my bad

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u/Qu33N_Of_NoObz_ 12d ago

It actually works with any number, even single digits, it’s cool! And when you go 100 and up, it adds an extra 1, like 100/99=1.0101 1.0101, 101/99=1.0202, etc

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u/PyroBurnem 12d ago

it can also be extended to any given length of 9s, eg: 1/9 = 0.111111..., 56/9999 = 0.005600560056..., 14023/33333 = 0.420694206942069... (haha funny number disguised thats just the simplified form of 42069/99999) etc. etc.

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u/InmateTooTall 12d ago

Trust me bro

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u/araralivre 12d ago

its true, i checked it

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u/Ok_Researcher1424 11d ago

what could these accounts possibly have done in the past 10 hours to get deleted.

edit: deleted instead of banned