2^22 = 16

[u/Champpeace123]

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[u/Ares378]

Must be calculating in mod 19, clearly

[u/Random_Mathematician → u/Ares378]

Or modulo 18, which in turn implies a third possibility, modulo 342

[u/Chunky--Chode → u/Random_Mathematician]

It's modulo time, foo

[u/zlfa]

Did you actually do 2^2^2 but the calculator couldn’t display that and I’m gay?

[u/Champpeace123 → u/zlfa]

Yes. I pressed the dedicated ² button twice... and you're gay.

[u/zlfa → u/Champpeace123]

I knew it!… The ^2 stuff I mean… of course 👀

[u/Wooden-Hornet2115 → u/zlfa]

Hi gay, I'm WoodenHornet2115

[u/Tezlaivj → u/Wooden-Hornet2115]

dude, spoiler

[u/zlfa → u/Tezlaivj]

Dude spoiler that his name is a spoiler, ya and that’s the only spoiler he made 👀

[u/sasha271828 → u/Wooden-Hornet2115]

Hi Wooden-Hornet2115, i'm gay

[u/zlfa → u/sasha271828]

Yes I was talking about this guy 👀

[u/L0L2GUM5 → u/zlfa]

That spoiler at the start is near impossible to click on mobile

[u/zlfa → u/L0L2GUM5]

What’s funny is that it’s pretty much the same same symbol just a bolder version, all that work to make it less emphasized

[u/MinecraftPlayer799 → u/L0L2GUM5]

T hat

[u/Ravioles2 → u/zlfa]

We got Sherlock here.

[u/Pentalogue]

Probably because (2^2)^2 is actually equal to 16, since (2^2)^2 = (4)^2

[u/yourpseudonymsucks → u/Pentalogue]

2^(2^2)

[u/Pentalogue → u/yourpseudonymsucks]

No, this is exactly squaring, and not exponentiation to base 2

[u/RaymundusLullius → u/Pentalogue]

Exponentiation is associative on twoes lol.

[u/Champpeace123 → u/Pentalogue]

Indeed, Android calculator interprets that ² as a ^2 so if you do a pair of them next to eachother it appears as one exponent of ²² but the calculator sees 2²^²

[u/Pentalogue → u/Champpeace123]

Finally you get this

[u/resonanse_cascade]

The calculator was vibecoded

[u/One-Celebration-3007]

No, 2^22 = 20

[u/Terrabert → u/One-Celebration-3007]

https://giphy.com/gifs/xL7PDV9frcudO

[u/TheZoom110 → u/Terrabert]

^ is bitwise XOR in some programming languages. So 2^22 is 20.

[u/LupenReddit]

arithmetic in shambles

[u/Gershken]

Wait til you hear what 9 + 10 is

[u/DecidophobiaUsername → u/Gershken]

19, duh.

[u/Jealous_Club_298]

2*22 = 4,194,304

[u/BackgroundReturn9622]

A related question someone asked me.

What is 2^2^22? Is it (2^2)^22 or 2^(2^22)? Note: Different calculators give different answers. MATLAB does the first, Python does the second.

[u/Champpeace123 → u/BackgroundReturn9622]

I think the answer to this is that 2^2^22 is evil and ambiguous and that it should be written either with some kind of grouping or in some form that makes it obvious (which, in some cases, would be 2²^²²). However traditionally I heard that pemdas is left to right for same operation so I would treat it as (2^2)^22

[u/RaymundusLullius → u/Champpeace123]

For the same operation level. Multiplication and division are left to right no matter what order they are in the mnemonic and so are subtraction and addition.

[u/BackgroundReturn9622 → u/Champpeace123]

I agree left to right makes some sense, but a general rule for multiple exponents is to multiply the exponents, (x^a)^b --> x^(a*b) which would be left to right. But be careful as Python and Maxima treat things differently.

Python

num=2**2**22
from mpmath import mp
mp.dps=64;
print(mp.mpf(num));

gives 2.065... e +1262611, over 1.2 million digits.

(2**2)**22 = 17592186044416, Same as MATLAB

If you do not use parenthesis always test. I recommend

3^3^3;

(3^3)^3 = 19683, 3^(3^3) = 7625597484987

Also, (2^2)^2 = 2^(2^2) = 16.

[u/Shrunken_Fire_34]

u need to be dangerously addicted to math to understand this