The BIGGEST Number

You might've overdone it, idk

>>>youtube.com/numberphile
>>>/highschool/

[math]1^1 \cdot 2^2 \cdot ... \cdot (10^{100})^{10^{100}}[/math]

I watch neither numberphile nor do I attend highschool, I don't get what you're trying to say

Only highschoolers don't know about knuth, only highschooler that watch numberphile know about knuth's arrow notation
put the two together and only a highschooler that watches numbersphile would think knuth's arrow notation is obscure as evidenced by "get on my level"
now kys underager

Googolplex*Graham's#^0

I'm always amazed at what internet strangers think they can learn from someone with such limited information. I'm a second year at U of T, doing analysis ii under the great Edward Bierstone

-1/12

C-(1/C)

Define by induction the following sequence of functions:
[math]f_0(n) = n+1[/math]
and
[math]f_{k+1}(n) = f_k^n(n)[/math]
where f^n is the function f composed n times with itself.

e.g.,
[math]f_1(n) = n + 1 + 1 + \ldots + 1 = 2n[/math] since "+1" appears n times.
[math]f_2(n) = 2 \times 2 \times \ldots \times 2 \times n = 2^n \times n[/math]
[math]f_3(n) \ge 2^{2^{\cdots^n}}[/math], a tower of exponentials of size n.

Now define:
[math]f_\omega(n) = f_n(n)[/math]
This is basically the Ackerman function.

We can go beyond: [math]f_{\omega+1}(n)
= f_\omega^n(n) [/math]

[math]f_{\omega+1}(64)[/math] is about as big as Graham's number.
The "use the Ackerman function with Graham's number" xkcd joke is actually just [math]f_{\omega+1}(65)[/math]

Define similarly [math]f_{\omega+k}[/math] for all k.
Define [math]f_{2 \omega}(n) = f_{\omega + n}(n)[/math]

We can keep going, define [math]f_{k \omega}[/math] for all k.
Then by the same process define [math]f_{\omega^2}[/math], then [math]f_{\omega^\omega}[/math].

Eventually we get to an infinite tower of omegas,
[math]\omega^{\omega^{\omega^\cdots}}[/math] which is called [math]\epsilon_0[/math].

[math]f_{\epsilon_0}[/math] grows about as fast as the Goodstein sequence.
[math]f_{\epsilon_0+1}(100)[/math] is bigger than the kinda famous TREE(3) number.

Of course you can keep going till [math]\epsilon_1[/math], [math]\epsilon_\omega[/math], [math]\epsilon_{\epsilon_0}[/math], an infinite tower of epsilons, etc.

being C the sum of the set of complex numbers

Graham's number is vastly larger.

the smallest number that cannot be defined in less than thirteen words

the opposite of the size of your penis hehe

doesn't hold if you have an innie

TREE(3)

ah so you saw the new numberphile video today?

im third year u of t

quit being such a dweeb we're not special for going to this school

I didnt understand your question so I will not answer it

[math]
ℵ_G
[/math]
Where G is Graham's number.

infinite+1

What's your native language? I'll translate for you

xiri language

that's a big number

Define [math] f(n):~\mathbb{R}^+\rightarrow\mathbb{N} [/math] to be the least integer [math] m [/math] such that [math] \frac{\varphi(m)}{m-1} < n [/math].
[eqn]
f\left(\frac{1}{\textrm{TREE}(3)}\right)
[/eqn]

TREE(4)

TREE(TREE(5))

TREE(10000)^TREE(100000)

TREE(TREE(5)) + 1

TREE(TREE(TREE(TREE(1000))))

TREE(TREE(TREE(TREE(1000)))) + 1

TREE(TREE(TREE(TREE(1000)))) + 2
BTFO
TT
F F
O F

itt: retards using digits that aren't 9

Why would you write 10 or 3 when you can write 99 or 9 instead

Anyway the obvious answer for a given number of characters is

TREE(TREE(TREE(TREE(...9

An innie penis?

this

TREE(TREE( ... (TREE(420) ... ))
where the length is TREE(3)

the size of my BBC.

You seem to have the 'tism. Be sure not to give it to other aspiring students

TREE(TREE( ... (TREE(420) ... ))
where the length is TREE(4)
Checkmate

fugg

his number plus one

BB^(BB(1000))(1000) where the ^(BB(1000)) part denotes functional composition and BB is the Busy Beaver function.

these two numbers added together plus one

Your number plus one half

damn

eleventy

This number to the power of
This number

that number plus three and six thirty-fifths

...

>any number you can fit on a white board
All numbers can fit on a white board.

[eqn]\infty[/eqn]

BIG FOOT

The smallest number that cannot fit on a white board.

Infinite isn't a number it's a concept

Let [math]x[/math] be number such that
[math]y \leq x < \infty[/math] for all [math]y \neq \infty[/math]

Can't get bigger than that tbqh famalam.

>all the branlets in this ITT

TREE(4U)

Let n be the sum of all the numbers in this thread.

10x10^125

this number + 1.

...

Let X be a number such that X > all number expressed on this thread.

Let X be the number of anons that didn't properly read the OP.

- BB^(BB(9999)) (9999)

take that, you're now the second smallest number ITT

1/infinitesimal

checkmate atheists.

Actually TREE(3) is way beyond that: math.stackexchange.com/questions/1950116/where-does-treen-sit-on-the-fast-growing-hierarchy

Let X = max{all number in this thread}
then TREE(X)
what now?

can you move to america, renounce your citizenship and never visit canada gain? youre making my county look like shit with how much of a fucking twat you are

Both are infinite recursions and therefore not well-defined, dumbass

Let X = X + 1

[math]\textup{Let } Y = \{x \in \mathbb{R} | x \in this thread excluding this post \}. \textup{Let }y = \textup{TREE}(\max Y)[/math]
Acceptable now?

My number is [eqn] your number + \lim_{n\to\infty}10^{-n}[/eqn]

Get rekt, kid

...

Extend [math]\mathbb{R}[/math] to [math]\bar{\mathbb{R}}=\mathbb{R}\cup \{-\infty,\infty\}[/math].

Boom, [math]\infty[/math] is a number now and it is the biggest number.
You're welcome.

[math]\lim_{n\to\infty}10^{-n}=0[/math], so you still have the same number as your #rekt friend, retard.

>Using the same name for two different things
Found the brainlet

OP doesn't say which space we're in, rETARD

Wrong.

Why then, dumbass?
OP only implies we're working in a totally ordered space with numbers.

underrated comment
what is it with this U of Tard and others like him thinking that drawing attention to himself and his lifestory on an anonymous imageboard will ever make up for never having anyone's respect irl

inb4 >you probably go to western

a brazilian

-(1/12)

>tried to make it
>failed to make it
my number is bigger because it exists :^)

Other comments are also recursively defined by other comments, so...
ill-defined [math]\implies[/math] you lost

Infinity is not a number. You could extend the real number line with whatever stupid shit you want to extend it with. That doesn't mean the things you added to the group become numbers.

Here's my answer
[math]Your number + 1[/math]

tree(3) fiddy

ur moms weight lmao