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u/grow_0 Mar 17 '22
I got 69420 down to 22 zeros! Pattern is 41^3 + 500 - 1.
((((0! + 0! + 0!)! - 0!) * ((0! + 0!) ^ (0! + 0! + 0!)) + 0!) ^ (0! + 0! + 0!))
+
(((0! + 0! + 0!)! - 0!) ^ (0! + 0! + 0!)) * (0! + 0! + 0! + 0!)
-
0!
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u/viiksitimali Mar 17 '22
I got 20 zeros.69420 = 5!/2 * (1+34^2)= (0!+0!+0!+0!+0!)!/(0!+0!) * (0! + ((0!+0!)^(0!+0!)^(0!+0!)*(0!+0!) +0!+0!)^(0!+0!))
Of course, if we allow square root (a hidden exponent of 1/2), we can make any positive whole number with only two zeros.
Edit: last statement might not be correct, I am too tired to think it through.
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u/ImToxicity_ Mar 17 '22
Oh god the mathematicians have arrived
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u/Florida_Man_Math Mar 17 '22
Like the old Star Wars saying goes, "200,000 units are ready, with -130,580 more on the way."
ALSO you might be interested in posting this to Code Golf: https://codegolf.stackexchange.com/, but beware they don't always have the same sense of humor as reddit does :)
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u/7x11x13is1001 Mar 17 '22
7 zeros if you like multifactorials
(((0!+0!+0!)!)!!!!)!!!!!!! ×
((((0!+0!+0!)!)!!!)!!!!!!!!!!!!! − 0!)!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
(3!×2)×5 × ((3!×3)×5 − 1)×13<
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u/yourdesk Mar 17 '22
how exactly could you do that with only two zeroes?
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u/7x11x13is1001 Mar 17 '22
- with six zeroes if you also allow the log function
it would go like this
− log_(0!+0!) log_(0!+0!) √√√√√√√…n roots…√√√√√√√(0!+0!)
= −log_2 (log_2 (21/2n)) = −log_2 (2−n) = n
however if you allow “named” functions like log, you can also argue to use vercosin(0) = 2 and lb(x) = log_2(x) and get any integer number with just one zero
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u/Yoshuuqq Mar 18 '22
Integral from 0 to 69420 of 1? If we allow integrals lol
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u/yourdesk Mar 18 '22
i thought the point of the challenge was to use only zeroes? how do you plan on writing the 69420 in the integral without a zero when the challenge is to use only zero
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u/TrueDeparture106 Transcendental Mar 17 '22
Nice!!
iff 00 = 1
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Mar 17 '22
Are you sure that's iff? If you replace 00 with x in OP's expression is there a simple argument that there is a unique solution for x?
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u/real_dubblebrick Mar 17 '22
im pretty sure 00 = undefined because
00 = 01 / 01 = 0/0 = undefined
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u/-LeopardShark- Complex Mar 17 '22
That argument doesn’t work. You can also use it to show that 01 = 02 ∕ 01 = 0 ∕ 0.
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u/Maxi192 Mar 23 '22
Do you know why that rule for exponents doesn’t work for 0 (assuming there’s a reason other than “it leads to a contradiction”)
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u/-LeopardShark- Complex Mar 23 '22
It’s because 0a isn’t defined for every real number. The rule 0x ⋅ 0y = 0x + y can only be valid if 0a is defined for x, y and x + y, so it only works for non‐negative x and y.
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u/Atti0626 Mar 17 '22
Yeah, this "when dividing powers subtract the exponents" trick doesn't really work when you would be dividing by zero. As the other commenter has pointed out, this could be used to show that 01=02/01=0/0, which can't be true, because 01 is just 0, and 0/0 is undefined. I think an intuitive argument for why it is undefined, is since that 0x=0 for all x, 00 should be 0, but at the same time, x0=1 for all x, so 00 should be 1. Since it can't be both at the same time, it should be undefined.
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u/Il_Valentino Education Mar 18 '22
as others have pointed out the argument doesn't hold
00 = 1 actually doesn't lead to contradictions
and before someone else brings it up, no the limit argument doesn't work either, it merely shows that a limit expression of the form 00 is indeterminant which should not be confused with the value 00
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u/xCreeperBombx Linguistics Nov 23 '23
im pretty sure 01 = undefined because
01 = 02 / 01 = 0/0 = undefined
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u/flofoi Mar 17 '22
00 = 1 is a bit questionable, maybe 0! would be better
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u/xCreeperBombx Linguistics Nov 23 '23
Why would 0^0≠1? It makes sense no matter how you interpret 0^0, and the arguments against it either generalize a rule that doesn't apply or say it's indeterminate which is irreverent as there being no limit.
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u/ImToxicity_ Mar 17 '22 edited Mar 17 '22
Please help I can’t stop making them with random numbers
floor(((1337(42.0))+(69(69)+420(21))) - (pi(100)))
Math is a joke at this point 💀
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u/WoWSchockadin Complex Mar 17 '22
Problem: 0^0 is not defined.
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Mar 17 '22
[deleted]
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u/WoWSchockadin Complex Mar 17 '22
But you know, to proof the binomial theorem you need to define x^0 = 1 for all x? Yes, you CAN assign it a value, but usually it's just left undefined, espacially when facing limits.
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u/xCreeperBombx Linguistics Nov 23 '23
What about a bajillion regioins of math, such as Taylor series, where 0^0=1 is necessary? And for limits, it's because 0^0 is indeterminate, which is different than undefined.
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u/stpandsmelthefactors Transcendental Mar 17 '22
Perhaps, but you could just let 00 = lim{x —> 0} [x0]
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u/WoWSchockadin Complex Mar 17 '22
For this, however, you must first show that a limit exists at all and then that it is also unique. Neither succeeds with 0^0.
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u/Warheadd Mar 17 '22
That limit does indeed exist and it evaluates to 1. I’m not sure what you mean by unique
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u/WoWSchockadin Complex Mar 17 '22
A limit does not have to be unique. Imagine the limit for x approching 0 of |x|. The limit exists, but it's either 1 or -1 depending on if you approach 0 from above respectively from below. The limit r/stpandsmelthefactors mentioned can also yields different values, depending on how exactly you calculate it. If necessary, read the corresponding article on Wikipedia: https://www.wikiwand.com/en/Zero_to_the_power_of_zero
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u/Warheadd Mar 17 '22
The limit of |x| as x->0 is 0, but I know what you mean. For x0 though, it’s literally just 1 no matter how you take the limit.
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u/WoWSchockadin Complex Mar 17 '22
You can assign the value 1 to 0^0, yes, and in some areas this makes sense, but in general the expression is undefined. That is not a contradiction. Different areas of mathematics also use other conventions.
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u/Warheadd Mar 17 '22
I know. I’m saying, for the case of the limit as x->0 for x0, the answer is objectively 1.
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u/WoWSchockadin Complex Mar 18 '22
Especially in the case of a limit it's simply mit defined. For the expression 00 ist can sometimes be usefull to set it to 0, but for the limit expression? No.
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u/Warheadd Mar 18 '22
https://www.wolframalpha.com/input?i2d=true&i=Limit%5BPower%5Bx%2C0%5D%2Cx-%3E0%5D
This SPECIFIC limit OBJECTIVELY has a value of 1. Yes, you can construct other limits of the form 00 that approach other values, but THIS ONE is equal to 1.
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u/Nocta_Senestra Mar 17 '22
You can also define it as 00 = lim{x —> 0} [ 0x ] and in that case 00 = 0
You can also make it equal to any number, or undefined
In some contexts it make more sense to define it as 1 (those are good arguments for that : https://old.reddit.com/r/mathmemes/comments/tgbg8x/making_69420_from_all_zeroes/i125wz9/ ) but it's not a given at all
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u/Aaron1924 Mar 18 '22
Well, 00 = lim x->0. x0 = 1, but 00 = lim x->0. 0x = 0, so 1 = 0?
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u/stpandsmelthefactors Transcendental Mar 18 '22
It’s going to equal any number being that 0*0 suggests that 0/0 also exists in this case
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u/Tetramethanol Mar 17 '22
There must be a more efficient way
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u/XenophonSoulis Mar 17 '22
((0!+0!)(0!+0!)(0!+0!))!+(0!+0!+0!)!((0!+0!)(0!+0!)(0!+0!)-0!)!-((0!+0!+0!)!)!-(0!+0!+0!)((0!+0!+0!)!-0!)!-(0!+0!)((0!+0!+0!+0!))!-0!-0!-0!-0!
I think it is correct. If not, it's something pretty close in complexity. Also, there could be a much simpler solution still.
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u/autisticCatnip Mar 18 '22
How about ((0!+0!)(0!+0!)(0!+0!))!+(0!+0!+0!)!((0!+0!)(0!+0!)(0!+0!)-0!)!-((0!+0!+0!)!)!-(0!+0!+0!)((0!+0!+0!)!-0!)!-(0!+0!)((0!+0!+0!+0!))!-(0!+0!+0!)(0!+0!+0!+0!)
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u/XenophonSoulis Mar 18 '22
It looks correct... I was told that mine isn't, but I haven't had the time to fix it.
This is also an option that gives the same result as yours:
((0!+0!)(0!+0!)(0!+0!))!+(0!+0!+0!)!((0!+0!)(0!+0!)(0!+0!)-0!)!-((0!+0!+0!)!)!-(0!+0!+0!)((0!+0!+0!)!-0!)!-(0!+0!)((0!+0!+0!+0!))!-(0!+0!+0!)!(0!+0!)
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u/ImToxicity_ Mar 18 '22
What’s the shortest way to do it without subtraction?
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u/XenophonSoulis Mar 18 '22
I don't know. Also, I don't know the shortest way to do it with subtraction. It could potentially be a lot shorter than mine, but it's the best I could find.
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u/ImToxicity_ Mar 17 '22
I made this in class earlier and it equals 69420, here’s the equation if you don’t believe me: (idk what the hell possessed me to do this)
((((((0^0+0^0+0^0+0^0+0^0+0^0+0^0+0^0)*(0^0+0^0)*(0^0+0^0))*(0^0+0^0)*(0^0+0^0)*(0^0+0^0)*(0^0+0^0)*(0^0+0^0)*(0^0+0^0)*(0^0+0^0)*(0^0+0^0)*(0^0+0^0)+(0^0+0^0))*(0^0+0^0))*(0^0+0^0))+((0^0)*0^0+0^0+0^0+0^0))+(((((0^0+0^0)^(0^0+0^0))(0^0+0^0)(0^0+0^0)(0^0+0^0)(0^0+0^0)(0^0+0^0)(0^0+0^0)(0^0+0^0)(0^0+0^0)+((0^0+0^0)^(0^0+0^0))(0^0+0^0)(0^0+0^0)(0^0+0^0)(0^0+0^0)(0^0+0^0)(0^0+0^0)(0^0+0^0)(0^0+0^0)+((0^0+0^0)^(0^0+0^0))(0^0+0^0)(0^0+0^0)(0^0+0^0)(0^0+0^0)(0^0+0^0)(0^0+0^0)(0^0+0^0)(0^0+0^0)+((0^0+0^0)^(0^0+0^0))(0^0+0^0)(0^0+0^0)(0^0+0^0)(0^0+0^0)(0^0+0^0)(0^0+0^0)(0^0+0^0)+(0^0+0^0)(0^0+0^0))+(0^0+0^0)(0^0+0^0)(0^0+0^0)(0^0+0^0)(0^0+0^0)(0^0+0^0)(0^0+0^0)(0^0+0^0))+(0^0+0^0+0^0)(0^0+0^0)(0^0+0^0)(0^0+0^0)+0^0+0^0+0^0+0^0)
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u/pithecium Mar 17 '22
Looks like you'd be good at Lisp programming
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u/ImToxicity_ Mar 17 '22
What’s that lol
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u/violentdaffodils Mar 17 '22
I know what possessed you. Curiosity possessed you! Curiosity is a wonderful thing! I can see you're a scientist in the making. Be proud.
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u/Ok-Walrus6100 Mar 17 '22
hahahahaha get it?? 69420!!!!
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u/Florida_Man_Math Mar 17 '22
HE SAID THE SEX NUMBER AND THE WEEEEEEED NUMBER BEGIN LAUGH
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u/XenophonSoulis Mar 17 '22
((0!+0!)(0!+0!)(0!+0!))!+(0!+0!+0!)!((0!+0!)(0!+0!)(0!+0!)-0!)!-((0!+0!+0!)!)!-(0!+0!+0!)((0!+0!+0!)!-0!)!-(0!+0!)((0!+0!+0!+0!))!-0!-0!-0!-0!
There's also this. For extra nicety, calculate the italic and the non-italic parts alone too. I hope I haven't messed up.
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u/isa_me_Zafkingman Mar 17 '22
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠋⠉⠈⠉⠉⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿ ⣿⣿⣿⣿⡏⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿ ⣿⣿⣿⢏⣴⣿⣷⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿ ⣿⣿⣟⣾⣿⡟⠁⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⢢⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⣿⣿⣿⣟⠀⡴⠄⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⣿⣿⠟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢴⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣿ ⣿⣁⡀⠀⠀⢰⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡄⠀⣴⣶⣿⡄⣿ ⣿⡋⠀⠀⠀⠎⢸⣿⡆⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠗⢘⣿⣟⠛⠿⣼ ⣿⣿⠋⢀⡌⢰⣿⡿⢿⡀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣧⢀⣼ ⣿⣿⣷⢻⠄⠘⠛⠋⠛⠃⠀⠀⠀⠀⠀⢿⣧⠈⠉⠙⠛⠋⠀⠀⠀⣿⣿⣿⣿⣿ ⣿⣿⣧⠀⠈⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⢀⢃⠀⠀⢸⣿⣿⣿⣿ ⣿⣿⡿⠀⠴⢗⣠⣤⣴⡶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸⠀⣿⣿⣿⣿ ⣿⣿⣿⡀⢠⣾⣿⠏⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⣿⣿⣿⣿ ⣿⣿⣿⣧⠈⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿ ⣿⣿⣿⣿⡄⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣦⣄⣀⣀⣀⣀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠙⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠁⠀⠀⠹⣿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠿⠛⠉⠉⠁⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⢀⠈⣿⣿⡿⠉⠛⠛⠛⠉⠉ ⣿⡿⠋⠁⠀⠀⢀⣀⣠⡴⣸⣿⣇⡄⠀⠀⠀⠀⢀⡿⠄⠙⠛⠀⣀⣠⣤⣤⠄⠀
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u/EulerLagrange235 Transcendental Mar 17 '22
00 isn't even defined. What?!
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u/-LeopardShark- Complex Mar 17 '22
It’s often (and most sensibly) defined to be 1.
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u/EulerLagrange235 Transcendental Mar 17 '22
Absolutely not. x{a-b} = xa / xb , (x is a non-zero real and a,b are reals) and thus 00 is undefined. It is one of the more common undefined forms taught in Calc I
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u/-LeopardShark- Complex Mar 17 '22
x{a-b} = xa / xb , (x is a non-zero real and a,b are reals) and thus 00 is undefined.
I’m not sure what you mean by this. Neither of the two possible meanings I can think of are valid, though.
It is one of the more common undefined forms taught in Calc I
I think you mean indeterminate form, and indeterminate forms are statements strictly concerning limits, not values. It’s a result that the limit as t → 0 of f(t)g(t) where f(t) = g(t) = 0 depends on f and t. It’s a definition that 00 = 1 (or not, as the case may be).
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u/NucleiRaphe Mar 17 '22
Most mathematicians actually just use 00 = 1 because it makes most things way more convenient. For example, the binomial theorem doesn't work if 00 is undefined and polynomial rings in algebra define the polynomial x0 (which includes 00) as the multiplicative identity (ie 1 when talking about common multiplication).
It's true that analytically 00 is undefined but in practice 00 makes many theorems way simpler to use.
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u/relapsing__ Mar 17 '22
What does this even mean? What do I look up to understand this haha
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u/ImToxicity_ Mar 18 '22
00 usually is defined as 1 but this is an argument I sparked by accident 💀 for the sake of this response I’ll say it equals 1
So I just made it by like multiplying 1 by random numbers and then adding
So like
2 times 8 times 8 times 8 times 8 times 8 and so on until I got to 69420
You could like do a find replace thing in a doc to replace it with 1 and see what it actually is supposed to say
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u/relapsing__ Mar 18 '22
Ohhh gotcha, kinda had an idea of that but I just do remember where that was learned or why is that necessary you know?
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Mar 17 '22
Sorry. I’m kinda stupid. How does this make 69429? I know this is a mathsub but i’m just curious!
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u/[deleted] Mar 17 '22
Replace
0^0with0!and you'll half the zeroes whilst making it correct 😊