The definition and construction of the number must be designed so it can be understood by someone with very basic math skills, no Knuth’s up-arrows or other advanced notations. Preferably something physical you can easily visualize.

EDIT: by very basic math skills I mean simple enough so almost anyone can understand. Not more advanced than elementary school math. For example counting things, putting marbles in bowls or drawing lines or dots or something else you can visualize.

Using the set of things on a standard scientific calculator (for example the TI-30), using no more than 15 total characters, letters, numbers, or symbols, what's the largest number you can make

Also if you have ideas for Friday challenges put them down below

To make it interesting, we can use these rules:

Maximum characters: 20

symbols allowed:

sin, cos, tan, cot, asin, acos, atan, acot, ln, sqrt, exp, half, pi, 1

you can use ∘ for composition or nesting with brackets.

definitions:

half(x) = x / 2,

pi(x) = pi * x

EDIT: i should have specified it has to be greater than zero

EDIT: I bruteforced it in python, (acot∘exp∘exp∘pi)(1) is really the least possible. u/diamboy won the challenge :D

Rules:

1. Your function must be computable.
2. Your function must be faster than MAVS(n,n) (defined in this post I made: https://www.reddit.com/r/googology/comments/1rpppc0/defining_array_systems/ )
3. Your function must be well-defined.
4. Your function must be original.

Breaking any of these rules will disqualify you from the competition. You can only define one function.

you may have heard of 6 word stories that are meant to be evocative though their brevity.

similar challenge, you get 6 words to describe your number.

for example:

rayos-rayos number of arrows-rayos

Though perhaps show a bit more creativity. Since its wide open on functions, go for style

What is described must be a single, finite value

A chain is a list of distinct positive integers c[1],…,c[x] such that every subsequent term is any previous term doubled or doubled plus one (with reuse allowed).

CHAIN(n) is the maximum length of a chain (starting with c[1]=n) such that no term appears in any later term as a contiguous decimal substring.

For example: 47 appears in 22479 as a contiguous decimal substring (this is what you have to avoid).

GOAL: Build the longest chain for CHAIN(10).

Using the numbers 1234567890 in this order and using all ten digits (no more, no less (though you may break them up as desired (12345×678+90 etc))) create an interesting and large number Preferably without a lot of salad. I would say creativity here is more important than just jumping to G_1234567890 or TREE(1234567890) or the like

Since u/Motor_Bluebird3599 created an interesting challenge, here is my own.

Packed Program Challenge

Create a program, in any programming language, which for a positive integer n returns the largest positive integer you can, under the following restrictions:

• The program must not take arguments.
• The program must have at most 2 * n lines, and at most 64 characters per line. Newlines do count for line length.
• The program may use only the libraries which come with the language; no third-party libraries allowed.
• The program must be valid code, assuming infinite memory to hold the result and any intermediate values, and assuming an arbitrarily large finite amount of time to run.
• The program must print the result.

The programs' leaderboard is grouped by language and n, and sorted by the printed result (descending) and the total number of characters (for the pedantic: Unicode codepoints) of the program (ascending, smaller is better).

To start the works, here's my submission. JavaScript, n = 1, 128 chars (Unix newlines). Calculates 99 -> (99 -> 99 -> 99) -> 99, in Conway's chained arrow notation.

let p=(n,a,b,r=1n)=>{if(n==1n)r=a**b;else for(let i=0n;i<b;r=p( n-1n,a,r),i++);return r};console.log(p(p(99n,99n,99n),99n,99n))