general

Baby fluid

first I need to aquire baby fluid

Cum

Cum is babyfluid

using only the basic operations +, -, *, /, and ^, is it possible to make a function that outputs '1' if input x = a, and '0' if input x != a?

I assume you do not want the obvious answer of a piecewise defined function

it would have to be a piecewise defined function now that I think about it, because what you are asking for is a function f(x) = 0 except at a, where f(a) = 1

there is no continuous way to do that

ooh pika, do you know simplex linear equations and stuff

i c

Yes hello

would it be possible for only integers though

no

it is actually not possible

let me draw you a graph

ooh I might throw some hw stuff here later

lmao

what you are asking for is this pirate

addition, subtraction, division (except with zero), multiplication, and exponents are all continuous operations

so any combination of them would yield a continuous function

this is not continuous

ergo, you cannot have a function made of those continuous operations that gives you what you want

tragic

If you allow piecewise functions its trivial

this only uses those operations (specifically none of them)

and is a function

I can make a function that arbitrarily approaches what you want though

my dreams and ambitions are already shattered so it's fine

although if you could make one that is 0/1 for whole numbers but continous between them

that would be a little cool at least

as d -> infinity, this will look more and more like what you want

that looks like this with d=100000

but when you zoom in its clearly not exactly what you want

this demonstrates the dynamics of the problem though

so full marks

what do you mean by 0/1

do you mean 0 or 1,

for every whole number besides 1 it's 0

feels like that would be possible

but it can be continous inbetween

so f(2) = f(3) = ... = 0

but f(1) =/= 0

well f(a) =/= 0, meant 1 as in one of the numbers

oh you are saying, for all integers except one integer a, f = 0

okay

uh

I am struggling to think of an example that would work for that. It cannot be a polynomial equation (except if you allow for an infinite polynomial)

for example

like, this would be zero for all positive integers greater than 1

I thought you made a penis there for a second

oh wait

i was asking about that because someone else I asked had come up with something

but turns out they cheated and used an infinite product

yes

that makes more sense

the graph of what I wrote is actually kind of ridiculous though

that is this

if you allow infinite sums instead of infinite products, and accept all integers being zero

taylor series for sinx but replace x with pi x

but I don't think there is a finite way to ensure it holds for all whole numbers

pirate why did this topic come up

there's a person in another server who asked me for 'ridiculous math problems'

the first one i gave was

actually the month/day/year thing from here

that one was fun

I still have that code

they ignored leap years so they were off by a bit

I ignored them too

interesting

leap years are a pain to code around

they said 26.9% of days would be unique

let me get my code

while yours was 29

iirc

oh you had that saved

still i wonder which one is the most accurate

I only ran it from year 1 to 2020