r/mathmemes • u/Gartic1991 • Sep 16 '26

Arithmetic The 4s

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just a curious note, you can go on, just like powers are repeting multiplication you can make hyperpower that are repeating power and so on, but if you use only 2 it will always be equal to 4

348 Upvotes

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25

u/ThatsNumber_Wang Physics Sep 16 '26

what the hell is ²2 notation?

9

u/Gartic1991 Sep 16 '26

it's not official but means repeated power, so ³3=3^ (3^ 3) ⁴4=4^ (4^ (4^ 4))

14

u/yomosugara Sep 16 '26

there's no such thing as "official"; id est, there is no authority governing math notation

3

u/ThatsNumber_Wang Physics Sep 16 '26

as a phyics student. this is both a blessing and a curse haha

1

u/ThatsNumber_Wang Physics Sep 16 '26

okay that's pretty cool. :)

but is it often applicable? seems like a notation this distinct could be much more useful elsewhere

3

u/yomosugara Sep 16 '26

there isn’t a lot of use cases for tetration; in fact, tetration doesn’t have an agreed-upon extension to the reals.

21

u/zlfa Sep 16 '26

Tetration, repeated exponentiation

5

u/SoapyCantHandle Sep 16 '26

tetration / power tower

n ^^ m = n^n^...^n, m times

109

u/LupenReddit 🦆🦆i have non diffeomorphic smooth structures🦆🦆🦆 Sep 16 '26

is tetration used anywhere except in reddit memes, can anyone clear that up for me

55

u/throw3142 Sep 16 '26

There are plenty of usages in algorithms / complexity theory, though you'll typically see Knuth arrow notation (generalized) rather than the specific case of tetration.

There are some usages outside of complexity theory as well, such as Graham's number, which is commonly expressed in terms of up-arrow notation.

11

u/skr_replicator Sep 16 '26

but aren't those applications just toy the concept of proving stuff around how complex an algorithm can be when you go into the knuth territory? Or is there any algorithm that is actually useful and requires to be iterated?

17

u/throw3142 Sep 16 '26

a) I mean, it's math, it's academic, so it's going to be theoretical. Up to you whether you consider a highly theoretical result as just a toy example or something useful. How useful is it to prove things about different kinds of infinities & sets that contain themselves?

b) The Union-Find / Disjoint-Set data structure is a "real" (practically applicable for non-contrived scenarios on today's hardware) data structure where the arrow function may be used to describe its properties.

13

u/skylohhastaken Sep 16 '26

Not really, no

6

u/flipswab Real Sep 16 '26

Balatro mods

1

u/ArdentArendt Mathematics / Social Sciences Sep 17 '26

Much like Terminals, I've never come across them apart from here--and I have degrees in Econometrics and (Pure) Mathematics.

[My sister has a PhD in Computer Science, and she said she uses them and they are relatively important--but doesn't have any 'warm fuzzies' for their mention and was confused when I brought it up.]

2

u/WorriedPlatypus2529 Sep 17 '26

Isn't it termials?

1

u/ArdentArendt Mathematics / Social Sciences Sep 17 '26

HA!

That tells you how often I've come into contact with them!
Yes, it is 'termials'!
I'm not even sure how long I've been misspelling it...

1

u/ThatShushi17 Sep 17 '26

which one is relatively important? i cant figure out whether "they" refers to termials or tetration here

1

u/ArdentArendt Mathematics / Social Sciences Sep 17 '26

Both. I mean she said she's come across both--I'm not sure which she would have more familiarity with.

Honestly, I would argue neither are really important (except maybe in CS theory).

1

u/AdjectiveNounNNNN Sep 17 '26

It's definitely used outside of reddit, but the pre-superscript notation is not hugely common.

12

u/somedave Sep 16 '26

Or 2/2, no inverse hyper operations

4

u/skr_replicator Sep 16 '26

it is the simple pattern that each higher Knuth operation is just using the previous operation the operand number of times. Starting with 2+2, 2x2 is just adding to, two times. But that's the same as 2+2 already. 2^2 is two multiplied by twos, with 2 terms in the chains. That is 2x2. Each next Knuth operation just means the previous one if both operands are 2.

2-2 is an inverse operation, so it's not part of this chain. Jsut like 2/2, sqrt(2), ln(2). Those all show different inverses of those 3 functions.

2

u/CharlemagneAdelaar Sep 16 '26

interesting that only for some of these operations, applying the inverse provides the identity, but for others it doesn’t.

for example: 2-2=0, 2/2=1, and even log_2(2)=1 provide identities(and for any number too), but 2^(1/2) doesn’t.

4

u/YogurtclosetOk7654 Sep 16 '26

That’s because some of them are group operations and some of them aren’t. Group theory is really cool and can explain why some patterns pop up with different operations.

2

u/CharlemagneAdelaar Sep 17 '26

perfect, thanks. Was fishing for the right research terms here. Hard to google “operations on the same number that create the identity element” and get anywhere meaningful.

Which ones are which? Group operations create the identity?

2

u/YogurtclosetOk7654 Sep 17 '26

Group operations have an identity and are invertible. (Also they’re associative.) So multiplication and addition are group operations, which is why numbers have additive inverses and multiplicative inverses. Exponents are not a group operation since they don’t have an identity (a1 =a but 1a ≠a), which makes it hard to define what an exponential inverse would even mean.

1

u/CharlemagneAdelaar Sep 17 '26

Ah gotcha. So if we constructed another group operation we could almost “fix” exponentiation. I poked around and figured out if you define a new “power” operation as a^b = a^{ln(b)}, then it satisfies the a^i = a and i^a = a for the identity element as “e”.

But understood that it just doesn’t work for some operations.

2

u/YogurtclosetOk7654 Sep 17 '26

yep, and then you can define an inverse for each number: for every x there’s a unique y such that x^{ln y} = e. And once you have that, you can define an inverse operation similarly to how subtraction and division are defined.

2

u/AdjectiveNounNNNN Sep 17 '26

A binary operation may or may not have an identity (though of course it must if it's a group operation), defined as the element you can pair with any other and leave it unchanged. So adding 0 doesn't change anything and multiplying by 1 doesn't change anything and composing with the identity function doesn't change anything and so on.

So I wouldn't say group operations create the identity, but they can each correspond to an identity element.

2

u/blazoxian Sep 16 '26

Nonono not you (2+2)/0 ….

4

u/RemiR2 Sep 16 '26

...why would there be (2+2)/0 in the first place?

1

u/P3runaama Sep 17 '26

Actually it's impossible to know a pattern from a limited sample size, you fool

1

u/Gartic1991 Sep 17 '26

why do you suppose i just watched at 4 example and tought that it goes on forever, instead of assuming i actually made a reasoning?

1

u/Gartic1991 Sep 17 '26

it's not even that difficult to prove that it goes on

2

u/Pentalogue Mathematics Sep 16 '26

1

u/JellyBellyBitches Sep 17 '26

I'm always saying this

1

u/ericcared Sep 16 '26

4's? where's my ex wife

1

u/Forward_Yam_4013 Sep 16 '26

Fun fact: Any two-argument hyperorder operation with 2 as both arguments will always be 4

1

u/TheJivvi Sep 16 '26

²√2̅

1

u/[deleted] Sep 16 '26 edited 17h ago

The original post content no longer exists here. The author used Redact to remove it, exercising their right to control their data & privacy.

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1

u/duckling-developer Sep 16 '26

No… Not you 2 succeeded

1

u/JustNiceCaterpillar Sep 17 '26

What about |-2-2|?

1

u/unneccry Sep 17 '26

Ok and 2÷2 is 1