An Awesome Infinite Tetration Stack.... #shorts

Check out the full episode on my main channel here:

#tetration #powertower #exponents #infinite #infinity #root2 #squareroot #squareroots #math #mathematics #numbers

Combo Class, taught by Domotro, is a crazy educational show where you can have fun learning rare things about math, science, language, and more! This is the channel for Combo Class SHORTS and EXTRAS - make sure you're also subscribed to the main Combo Class channel where full episodes go!

DISCLAIMER: any use of fire, tools, or other science experiments in this series is always done in a safe and professional way. Do not try to copy any actions you see in this series yourself.

[Domotro]

Check out the full episode about tetration and further operations here:

[jamesschoon]

Very cool. My electronics professor showed us how to work this out using a power tower of x(i.e. x^x^x^x^... = 2), basically just a bunch of x exponents in one long chain which are equated to 2. Because the number of exponents on top of the first x tends to infinity, one could represent these exponents on top of the first x as approximately equal to 2, substituting the value(2) of the power tower onto that x . Therefore the equation simplifies to x^2 = 2 and then x = root(2). So one could conclude root(2)^root(2)^root(2)^... = 2. Excuse my first-year level reasoning in my explanation of it.

[apollopc]

Elegant as always. This example is so beautiful.

[EastNorthEast]

I love your videos!! This stuff is so fascinating and I dig your style

[alexschlessman]

There's a line in Futurama where Leela says " damage report: we've taken on a lot of clocks.
Yeah this guy has a lot of clocks

[OrangeDrink]

Very nice, 1 forever is 1 but .9 repeating would be zero, and 2 with infinit zeros ended with 1.... equals 4 and infinite ballanced.

[Admiralty]

Was this filmed in Captain Hooks cabin?

[jordanloveless]

You've gotta be a special kind of psychopath to know and love mathematics like this guy. I'm amazed every time I watch these clips.

[jo_de_pro]

I saw someone saying this once
Q2 = square root of 2

(A^B)^C = A^BC (basic math rule)

(Q2^Q2)^Q2 = Q2^(Q2×Q2)
(Q2×Q2 = 2)
Q2^2 = 2

So (Q2^Q2)^Q2

But during me writing this I realised

(Q2^Q2)^Q2 ≠ Q2^Q2^Q2

Thats why I do get to 2 with just 3 Q2's

This was shown in a video in a part about irational numbers in a proof showing that irrational numbers can make rational numbers

(The video was about why pi^pi^pi^pi... might be a rational number)

[Silentkidgaming]

How do we know it's approaching 2, why not 1.98 or something?

[cslloyd]

Its the Tango of tetration. It takes 2 to tango.

[gregfeneis]

The limit as we approach infinity powers of two is peace, bro.

[VidNudistKid]

If x = lim √2 tetr to n as n → ∞, then √2 ^ x = x. I'm not sure how one would solve this if the solution isn't already known, but confirming that x = 2 is a solution is trivial.

[davefoxxo]

Is this true for other numbers as well?

[brucecombs]

I have zero comprehension of why this is the case.

[dozenalmath]

"approaching infinity" how close can we ever get, really?

[jsraadt]

How do you notate the limit, or just how to notate tetration?

[Sn-zP]

If to the tenth tetration is 1984 then what's it to the 11th? Heaven ?

[pfpublius]

But what can we do with this? It is really cool, and it feels like it means something...but what?

[FewVidsJustComments]

So the square root of 2 to the infinitith power is the same as just squaring it. Weird flex but ok