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#math #brithemathguy #tetration

Corrections:
4:11 x = e^W(ln4) (not just W(ln4))

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[symmetricfivefold]

damn that function is wild 💀
never seen such fascinating way to use it inside a function before.

[symmetricfivefold]

way to calculate this:
4^8=2^(2^2(^2^(2)))
so 4^8=⁴2
so ²x to 2 =⁴2 ->²x =4 ->x=2

[duukvanleeuwen]

Wait until you try to do tetration with non-integers..

[Xiphius]

Do we learn this in school, like, ever?
If not, this channel deserves more recognition.

[Kaizite]

silly Bri. you made a mistake at the end. you perform the lambert W function to both sides after getting "ln(x) * e^ln(x) = ln(4)
W(ln(x) * e^ln(x)) = W(ln(4))
ln(x) = W(ln(4))
x = e^W(ln(4))
you said that x = W(ln(4)), but that's not true.
also, you can simplify e^W(ln(4))
ln(4) = ln(2^2) = 2 * ln(2) = ln(2) * e^ln(2)
so W(ln(4)) = W(ln(2) * e^ln(2)) = ln(2)
e^ln(2) = 2

so you got the same answer you got originally, which is x = 2.

[gdid]

The height of the tetration can also real.
x tetrated to y =
1 + x if -1 <= x <= 0,
x^(x tetrated to (y-1)) if x > 0
log_x(x tetrated to (y+1)) if x < -1
This is the linear approximation of tetration, which is continuous everywhere but not differentiable everywhere unless x = e.
For example, 2 tetrated to 0.5 can be approximated as 1.41421 using the linear approximation, which is close to the actual value of ~1.4587818160364217.

There are analytic approximations for tetration, but they are more complex.

[Ostup_Burtik]

Yes!
But what about non-integer tetration? What is i^^½ or i^^i? What is 0^^i?

[nishyanthkumar]

nice video!
i only knew about tetration because of bprp :D

[scottleung]

I've never seen or learned about this notation before, but it's interesting!

[bojankassebaum]

Hey Brian, I think you made a mistake in the last line... there is "x = W (ln (4))", but it should be "x = e^W (ln (4))". Please double check that and correct me if I'm wrong. 👍

[_crypt]

Welp time to differentiate the 2nd tetration of x

[austinturner]

I wonder what happens if you put non-integers as the power of a tetration

[Skank_and_Gutterboy]

3^4 is not 3 multiplied by itself 4 times. If you did that, you'd be calculating 3^5. It's more accurate to say that for 3^4, you're using 3 as a factor 4 times in your multiplication.

[GiveawayGamer]

Second answer is not fully correct..
It will be
e^(w(ln4))

[SixtyStone]

you dont efen need to remove the base at 3:33 i instantly reconiged x = 2.

[averagemusicproducer]

new math update changelogs:
added more confusing math

[IkumieIkupi]

Are u know the Knuth Arrow, Gijswijt sequence

[tsa_gamer]

The final answer should be e^W(ln4) because our lhs will become lnx after operate the W

[bbernyy]

hot take: tetration is a waste of time, and just a byproduct of people thinking oh, you go from repeated addition to multiplication, to exponentiation etc. so there must be something after it! Nope, (2^a)^b (the correct notation) equals 2^(ab). There is nothing following exponentiation.

[АннаСивер-гм]

Everybody now knows about tetration, for some reason.It seems to be literally everywhere.