pls help me thank you!

[sturdy ingot]

pls help someone asap

[broken peak]

What do you need to do?

[stone condor]

So it's 1+1/2+1/3+1/4.....
So 2 Idk whats n^s

Its approaching 2

And having absolute>1

So it's 2

[broken peak]

This sum is not 2?

it diverges

[stone condor]

First , what does n^s mean

[broken peak]

That thing is definition of zeta function

[stone condor]

I see

[broken peak]

it's defined correctly

there is nothing unclear about it

[stone condor]

So I'm far off from being correct on it being 2

[broken peak]

yeah

infinitely far

[stone condor]

But

Its decreasing

Its value

[broken peak]

Yeah

[stone condor]

It can't be > 3 for sure

[broken peak]

Huh

how do you know that

it's diverging

you know integrals?

[stone condor]

As it increases infinitely, its also decreasing infinitely

[stone condor]

Ye

[broken peak]

lemme show you example

[stone condor]

Sure hmm

[broken peak]

sorry forgot values

Do you want proof why it's infinity

[stone condor]

Oh hmmmm

So it's infinitely increasing hmmm

But the speed of decreasing value is also increasing

[broken peak]

When you group it by 1, 2, 4, 8, 16, 32 terms it's always greater than 1/2

so it's same as 1+1/2+1/2....

[stone condor]

Oh yea

[lapis scroll]

Its 51 I think

[broken peak]

How?

[stone condor]

If we do z(∞) =? Hmm

[broken peak]

z or zeta?

[stone condor]

From this

Function

[broken peak]

z(infinity) (as I defined it) is undefined

aka infinity

[stone condor]

Hmmm i see

[broken peak]

wanna also proof by integral

[stone condor]

What make it different when we add Zeta function

[stone condor]

Sure

If u have it?

Integral would be the best proof to it

[broken peak]

The red function is 1/x, and the boxes are representation of the sum 1+1/2+1/3...

Now integral of 1/x is ln(x)

so ln(infinity) < z(infinity)

and ln(infinity) is obviously infinity

[stone condor]

But i still feel like it has a limited value

But its countable infinite

[broken peak]

Lol throw your intuition away

[stone condor]

So a border but it's still infinite

[stone condor]

Well true , math proof is better

[broken peak]

What does countable infinite means in terms of number?

[stone condor]

Like

Between

[broken peak]

countable infinite is usually used for sets

[stone condor]

0 to 1

[broken peak]

is uncountably

for reals

[stone condor]

It has countable infinite numbers

But we still know it ends at 1

We know the border

Range

Like here

Its value keeps decreasing

Somewhere

It should decrease so much that

[broken peak]

Wait, you are claiming that interval from 0 to 1 has countably infinite real numbers?

[stone condor]

It creates a undefined border

[stone condor]

Incountably

But we know sum of all the incountable group

Hmm anyways

[broken peak]

Huh

[stone condor]

That

[broken peak]

whats the sum

[stone condor]

1+1/2+1/2

....

[broken peak]

.-.

[stone condor]

Is already infinite

[stone condor]

1

[broken peak]

So sum of all numbers between 0 and 1 is 1?

I dont get this

[stone condor]

Yeah

Like

Take natural numbers for example

From 0-10

[broken peak]

0+0.5+0.75 is already over 1

[stone condor]

WAIT WHAT

OH YEAH

[broken peak]

lol man

the sum would be infinite

[stone condor]

💀

[broken peak]

Actually, even sum of all numbers in interval (0, 0.0000001) is infinite

[stone condor]

0 - 1/∞

[broken peak]

Wdym

[stone condor]

Should be 1/∞ ?

1/∞ is the closest value to 0

Its reaching 0

[broken peak]

wait what

you just seriously defined closest value to 0

[stone condor]

Lol

I mean

We can't really use ∞ as number

[broken peak]

agreed

[stone condor]

but just saying

If we take a fake

Closest number to 0

Then will the sum be ∞

Or will it be = the closes value to 0

[broken peak]

Define such a number

good luck

[stone condor]

1/0

[broken peak]

.-.

Have you ever seen hyperbola?

[stone condor]

ye

[broken peak]

limit as x approaches 0 from right of function 1/x is infinite

or better, undefined

and from left it's -infinity

so whatta hell is 1/0

[stone condor]

Well yeah

[stone condor]

Lol , i just said that , that makes no sense

[broken peak]

It makes absolutely no sense

even saying it's infinity makes no sense

[stone condor]

True

But its touching the x at ∞

And y

[broken peak]

and also at -infinity...

[stone condor]

Yeah

[broken peak]

Function is set of all ordered pairs <x,y>

[stone condor]

Hear me out

[broken peak]

One value of x cannot have 2 ys

okay

[stone condor]

So it reaches +∞ and -∞ at x and y so ∞-∞ = 0 so its reaching closest to 0

[broken peak]

lmao

[stone condor]

Lol jk

Ok gtg , btw i have a #help-form , https://discord.com/channels/268882317391429632/1073311287716614184

I'm off by 1