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petStorm
petStorm
12:41 AM
10 hours later, I'm back!
 
Lyxal
Lyxal
@petStorm Nice
{x|x=x}
Is that just an infinite list?
Because it's all x where x = x
{x|x=x*2} -> {0}
{x|x=x^2} -> {0, 1}
 
petStorm
petStorm
@Lyxal It's an infinite list (U, I can't type the character).
U means the set containing all possible values.
 
Lyxal
Lyxal
{x: 0≤x≤2} -> {0, 1, 2}
 
petStorm
petStorm
(It's technically impossible to implement physically.)
 
Lyxal
Lyxal
CMC: Find an expression that produces the set {0, 1, 2, 3} that doesn't use limits.
 
petStorm
petStorm
12:45 AM
Uhh, boring answer... {0, 1, …, 3}
 
Lyxal
Lyxal
{x:x∈{0, 1, 2, 3}} another boring answer
 
petStorm
petStorm
@Lyxal Not neccesarily. Remember that there are decimals between these values!
 
Lyxal
Lyxal
Not-so-boring-answer: {x:x(x-3)(x-2)(x-1) = 0}
@petStorm {x: 0≤x≤2, x∈Z}
 
petStorm
petStorm
@Lyxal Okay, now you got it right.
 
Lyxal
Lyxal
CMC: {0, 4} without using digits 0 and 4
 
petStorm
petStorm
12:49 AM
{x|x∈Z,-1<x<5}-{1, 2, 3}
 
Lyxal
Lyxal
{x:x(x-5-1)=|ø|}
 
petStorm
petStorm
I have to get used to the maths.
Wait, you used 0 here.
 
Lyxal
Lyxal
|ø| = 0 right?
 
petStorm
petStorm
Right.
 
Lyxal
Lyxal
{x:x(x-5-1)=|ø|}
Nothing but a simple quadratic
 
petStorm
petStorm
12:56 AM
I can't think of a good CMC...
@Lyxal I guess this is 1 byte shorter: {x:x²-5x+x=|ø|}
 
Lyxal
Lyxal
CMC: {-1} without digits or +-*/%. Have fun with that one!
*Mathematical constants are allowed
 
petStorm
petStorm
{i²}
 
Lyxal
Lyxal
Ah.
Solved in 5 bytes.
Hmm.
{x:x=cos(π)}
That was my idea
Good 'ol trig
 
petStorm
petStorm
Probably just {cos(π)} would be valid.
 
Lyxal
Lyxal
Okay, this is a hard one:
CMC: {1.24027415108} digitless, sans +-*/%|
*Mathematical constants still allowed
GLHF
It's doable
But requires a little thing called calculus
{\int_e^π x dx}
;P
 
petStorm
petStorm
1:08 AM
CMC: Produce a decimal starting with {1.253815480...}, only with 2, with +-*/% banned.
I calculated that value totally using Windows calculator.
(Evidently it's completely arithmetic.)
* Mathematical constants allowed.
Well, that one is too easy. I retract that one.
@Lyxal CMC: Produce {2.6810600010025946269529585983025...}
Like the previous ones, digits are totally banned, as well as +-*/%.
* Mathematical constants are allowed.
Hint, I calculated it on my Windows desktop calculator. So it's totally arithmetic.
I got an 8-byter over here, GLHF.
 
petStorm
petStorm
1:40 AM
@Lyxal Did you solve my CMC?
Anyway, I'm going to leak my answer: √(π!)
 
Lyxal
Lyxal
1:56 AM
I would not have gotten that one
CMC: {3} using only 0x+^
@petStorm no because I was too busy simulating binary addition and subtraction with rocks
 
petStorm
petStorm
{0°+0°+0°}
If we can use cardinality this would greatly simplify the question.
 
Lyxal
Lyxal
@petStorm 0^0 is undefined though
So it'd be x^0 x≠0
 
petStorm
petStorm
@Lyxal Where does the ≠ come from then?
Ugh, I can't solve it.
 
Lyxal
Lyxal
@petStorm looks like I forgot a symbol
@petStorm wait how is there a factorial?
 
petStorm
petStorm
@Lyxal Because I used Windows calculator. The calculator is very weird...
 
Lyxal
Lyxal
2:03 AM
IIRC, Factorials don't work on decimals
 
petStorm
petStorm
Windows calculator allows you to take the factorial of a decimal...
That's why I gave you the hint.
 
Lyxal
Lyxal
@petStorm b...b...but I use macos
And my phone is Android
So I'm kinda unable to use a Windows calculator without finding and charging my Windows first
 
petStorm
petStorm
This allows you to take the factorial of a decimal.
I'm not sure if this produces the correct result though.
 
Lyxal
Lyxal
But how does it work? The factorial taking that is.
 
petStorm
petStorm
I have absolutely no idea.
(Yep. That one produces the correct result.)
 
Lyxal
Lyxal
2:08 AM
13
Q: How do we calculate factorials for numbers with decimal places?

Rohinb97I was playing with my calculator when I tried $1.5!$. It came out to be $1.32934038817$. Now my question is that isn't factorial for natural numbers only? Like $2!$ is $2\times1$, but how do we express $1.5!$ like this?

factorial gamma-function
Apparently it's possible
 
petStorm
petStorm
:)
So it's not just me.
*α?R
I gotta change the conditional system.
All numbers <= 0 are falsy, all numbers >0 are truthy.
?R* 
?   If input 1 is not true,
 R  Reverse the second operand (implicitly appended).
  * Multiply the reversed second operand by the first operand.
34
Q: Multiply a string by a number!

GryphonThere was a challenge up a while ago about multiplying strings. It showed us how we can multiply not only numbers, but also strings. However, we still can't multiply a number by a string properly. There has been one attempt to do so but this is obviously wrong. We need to fix that! Your Task...

code-golf string number arithmetic
Solving this question...
 
Lyxal
Lyxal
2:56 AM
@petStorm *falsey
There's an e in falsey
It can be both
@petStorm That is a weird definition of falsey and truthy just for one challenge.
Are there other scenarios where this definition would help?
 
petStorm
petStorm
Uhh, not really.
 
 
3 hours later…
petStorm
petStorm
5:48 AM
CMC: Generate the set of all possible matches of 0+1+, assuming that you are allowed to repeat a set.
Spoiler first: {rep(0,x)|x∈N}×{rep(1,x)|x∈N}
 
petStorm
petStorm
6:24 AM
I guess I'll try to solve Fizzbuzz in NST, as a comparison with Vyxal.
 
Lyxal
Lyxal
@petStorm I thought you already had
 
petStorm
petStorm
First, copy some canvas characters over here. Ｈ stands for one hundred, ║ generates a range to 1.
(You know, weird character choice.:) )
Ｈ║|3÷‾5÷2∧Fizz,BuzzƤ‾∨
Awww, it's 22 bytes... 4 bytes longer.
Wait, NST has Jelly's logical or hook! Ｈ║|3÷‾5÷2∧Fizz,BuzzƤ∨
Also, it pretty much has an implicit 1-range (inherited from W/Stax). Ｈ|3÷‾5÷2∧Fizz,BuzzƤ∨
Dictionary from MathGolf. 17 bytes (┘ is capitalization): Ｈ|3÷‾5÷2∧θ#,θ@┘Ƥ∨
Fix the order. Ｈ|35,÷TSθ#θ@,┘Ƥ∨
16 bytes: Ｈ|35,÷┬Σθ#θ@,┘Ƥ∨ ┬ gets all truthy indices. In NST only single-digit constants can be pushed.
 
 
2 hours later…
Lyxal
Lyxal
8:44 AM
How do I check for primality?
I'm thinking something like {x:factors(x)={1,x}}
But that feels like cheating
 
petStorm
petStorm
@Lyxal {a:a∈N,{x:x∈N,x>0,a%x≠0}={1,a}}
The list of all prime numbers.
 
Lyxal
Lyxal
@petStorm then add a x in to the front
 
petStorm
petStorm
@Lyxal What do you mean? Can you post the modified code?
 
Lyxal
Lyxal
8:59 AM
@petStorm I mean to find if a number is a prime or not
You say "is the input in the set of primes"
 
petStorm
petStorm
α∈{a:a∈N,{x:x∈N,x>0,a%x≠0}={1,a}}
 
Lyxal
Lyxal
Yes
Like that
 
petStorm
petStorm
Assuming N = {1, 2, 3, ...} this can be shorter.
α∈{a:a∈N,{x:x∈N,a%x≠0}={1,a}}
Even shorter: α∈{a:a∈N,{x:x∈N,a∤x}={1,a}}
Same length. α∈{a:a∈N,|{x:2<x<a,a∤x}|=0}
Fixed a bug.α∈{a:a∈N,{x:x∈Z,2<x<a,a∤x}={1,a}}
Ugh, now I've ended up bloating this program by 1 byte!
 
 
2 hours later…
petStorm
petStorm
11:20 AM
I just found a book in my house with an awesome tutorial of the set theory.
 
 
2 hours later…
petStorm
petStorm
12:56 PM
Sets are capable of representing functions.
E.g. Add the input by 1, the set can be represented as: {{0,1},{1,2},{2,3},{3,4},...}
And then, to call that function (the above set is X): {Y|{X,Y}∈X,X=α}, where α is the operand of your function call.
 
petStorm
petStorm
1:34 PM
A function is a set of pairs. The domain (all possible inputs) of a function is defined as follows:
dom(f) = {x|{x,y}∈f}
And the range (all outputs from possible inputs) is defined as:
ran(f) = {x|{x,y}∈f}
Wait, it's set theory.
Set theory has these tuples that are order sensitive, unlike sets.
Its syntax is (x,y).
dom(f) = {x|(x,y)∈f}; ran(f) = {x|(x,y)∈f}
A function is like this: {(0,1),(1,2),(2,3),(3,4),...}
I can't understand the rest of the tutorial, I'll try again tomorrow.
CMC: Define a successor function.
(Just to challenge myself.) {(X,X+1)|X∈Q}
 

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