What Do We Do Math If Math Is Already Exist ?

[marble oasis]

⎡ cos(φ)·cos(θ) ⎤
⎢ cos(φ)·sin(θ) ⎥  
⎣    sin(φ)     ⎦

because with the physics and math we can create everything, look, this create an sphere

and if you want to incline the earth, this is this :

⎡ cos(α)  -sin(α)  0 ⎤
⎢ sin(α)   cos(α)  0 ⎥
⎣   0        0     1 ⎦

with we math we can explain like, everything is this universe at 99.99%, this is why we do math

for put an write on a thing we cant explain by an other path

[gray drum]

i will do you one better: R=3

i mean

[marble oasis]

https://tenor.com/oEujYUzgmeF.gif

[gray drum]

${|x|=3\big| x\in\mathbb R^3}$

[marble oasis]

average little shitty cornass in this planet

[gray drum]

ahhhh too big

[hushed yarrow]

Tangent

[gray drum]

alr

[marble oasis]

more better

pls <@&268886789983436800> ban this shitty little troller dumbass

[gray drum]

more better: ${x\in\mathbb R^3\big|$ x is on the wanted sphere$}$

[hushed yarrow]

Tangent

[gray drum]

me?

[granite folio]

Incredible

[marble oasis]

thx mod 🙏

[gray drum]

oh not me ok

[marble oasis]

no, the other spammer

[lyric pebble]

What a polite way to ask for that too

[gray drum]

ok

[granite folio]

At least he spammed in a place basically noone looks

[gray drum]

lol

[marble oasis]

ohh yeah

but R is not a packet of infinite ?

[gray drum]

wdym

[marble oasis]

i have heard somewhere than R is a packet of infinite, so this is not a good geometrical value ?
-# i have surely wrong because idk really this domain

[gray drum]

im not sure what does "a packet of" means

[hushed yarrow]

Tangent

[marble oasis]

idk too, the guys said than when infinite is not enough, we do value like R than is a bigger infinite composite of infinite, and he represented him with a bag with infinite in him

[gray drum]

like

$|\mathbb R|=\aleph_1$ and $\infty=\aleph_0$?

[hushed yarrow]

Tangent

[marble oasis]

ohhh yeah this is it

the guys really bad explain and after i have not research by myself for more explain

[gray drum]

basically $\aleph_0$ is countable and $\aleph_1$ isnt

[hushed yarrow]

Tangent

[gray drum]

for explanation, do we agree that $\aleph_0$ is countable?

[hushed yarrow]

Tangent

[marble oasis]

yeah ? maybe

[gray drum]

i mean $|\mathbb N|$ which is by definition $\aleph_0$

[hushed yarrow]

Tangent

[gray drum]

like, you can count to this infinity

0, 1, 2, 3, ...

[marble oasis]

yeah, this is a serie to 0 to infinite (but infinite is only a theory, so there is a limit in a moment)

[gray drum]

yes

so, if we count [the size of the set] 0, 1, -1, 2, -2, ... we get to the same infinity

[steep nest]

if i remember correctly the proof was something about listing all possible reals and then looking at the diagonal changing just to the next number and it still gives a number that is not present anywhere

[gray drum]

yeah thats where im weak i dont remember the proof $\aleph_1\neq\aleph_0$

[hushed yarrow]

Tangent

[gray drum]

would like to hear it too

[marble oasis]

no, like -∞ is a negative infinite and ∞ is a positive infinite

[gray drum]

yeah i meant |{0}|, |{0, 1}|, |{0, 1, -1}|, ...

[marble oasis]

oh yeah for sure

[gray drum]

so that means $|\mathbb Z|=\aleph_0$ as well

[hushed yarrow]

Tangent

[marble oasis]

yeah

[gray drum]

ok now we know $|\mathbb Q|=|\mathbb Z|^2$

[hushed yarrow]

Tangent

[marble oasis]

yeah, but |Z|² do |Z| * |Z| so this do aleph2 no ?

[waxen trench]

It turns out |Z|^2 = |Z|

= aleph_0

[marble oasis]

ohh, this is because |Z| is already at his absolute, so he cannot be bigger than his max ?

[waxen trench]

I don't know what you mean by his absolute.

but the reason is more subtle.

There are larger infinities than Aleph_0

for instance, the cardinality of the reals is Beth_1 = 2^|Z|

[marble oasis]

i have learn (because him autodidact), than when there is this : |value| this is considered by the absolute or the cardinal of this value, i have wrong ?

[marble oasis]

ohhh, i understand, sorry if i take time to understand something 😅

[waxen trench]

And for any infinity we can construct a larger one.

so when we consider the cardinalities of infinite sets, if we can construct a function that maps each value of one to exactly one value of the other, and cover each value of the destination set (what we call a bijection), then they are the same size.

So the reason why |Q| = |Z| is because we can construct such a function.

(But the exact method to construct a function is not something that's easily expressed as a formula)

[marble oasis]

wow, this look impressive, me i learn more in the quantic, but this part of physics look very cool too 👍