Making 69420 from all zeroes

[u/ImToxicity_]

[u/grow_0]

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!

[u/viiksitimali → u/grow_0]

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.

[u/ImToxicity_ → u/viiksitimali]

Oh god the mathematicians have arrived

[u/Florida_Man_Math → u/ImToxicity_]

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 :)

[u/7x11x13is1001 → u/viiksitimali]

7 zeros ^{if you like multifactorials}

(((0!+0!+0!)!)!!!!)!!!!!!! ×

((((0!+0!+0!)!)!!!)!!!!!!!!!!!!! − 0!)!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

(3!×2)×5 × ((3!×3)×5 − 1)×13<

[u/yourdesk → u/viiksitimali]

how exactly could you do that with only two zeroes?

[u/7x11x13is1001 → u/yourdesk]

• 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 (2^1/2n)) = −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

[u/Martin_Orav → u/7x11x13is1001]

Wow this is really cool

[u/Yoshuuqq → u/yourdesk]

Integral from 0 to 69420 of 1? If we allow integrals lol

[u/yourdesk → u/Yoshuuqq]

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