# Kill the Mathematical Hydra | Infinite Series

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# Kill the Mathematical Hydra | Infinite Series

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100 thoughts on “Kill the Mathematical Hydra | Infinite Series”

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Career In Forensic Science

#hydragetrekt

why use ordinals if we are counting the number of heads?

Ima smash it with rocks.

The presenter is soooooooo cute!!!!

2:30 woah

So when there are ℵ₀ items in a list, the last item is the ω-th?

Disclaimer:

No Hydras were hurt in this video….

If it shares my physical universe then I give it too many heads ti sustain itself and it cannot function. Then burn it.

9:09 and 9:49, why the order in the 9:49 is different? I mean, am I counting things wrong or have I missunderstood something on the way? I mean, these two are practically identical if we ignore that one head in the first one, so why the second one (at 9:49) isn't omega ^ omega ^ 3?

Thermo-nuclear ballistic missile ought to do the trick 🙂

Prove that:1+1+1+1+1+1+1+1+1 ….. Upto infinity equals -3/4

Found an error at 4:31, the hydra on the right should have 26 heads on each of the three necks, you drew 27 instead

This sounds like a cool game to play

Really nice video! I think there is an error, though: in 8:04 you claim that the well ordering theorem implies that any decreasing sequence of ordinals eventually goes to zero, but the theorem only gives us an "abstract" well ordering, that isn't related to the order imposed by ordinals by Є. The claim you say follows from the fact that all ordinals are well orders (so that any decreasing sequence is contained in the succesor of the first ordinal of the sequence, and then eventually halts). And you can prove that all ordinals are well orders just using the transitivity property and a little bit more, maybe.

7:33 add a new thing that comes after all of them. As you said ordinals don't describe sizes but order…

Hello lady sorry I don't know your name but this should not stop me from asking this I have a question and the question is"why we only have a number system of even numbers like binary 0 and 1 decimal 0 to 9 octal 0 to 7 and even hexadecimal 0 to 16 or F why don't we have a number system with three numbers like 0 ,1and2 we can explain all numbers with help of these three numbers then why only even if you have read this comment please upload a video on this topic thank you have a nice day

so, infinity exists after all! because the fact that every hydra is eventually defeated no matter what you do is super intuitive, so infinity MUST exist!!!

This hydra is much easier to kill than a normal one. Normal hydra has no heads that can be chopped off without spawning new heads.

I hate it when mathematics explanations skip steps — even the simplest ones…just annoying. The animation does this, too, "visually jumping" a bit when something "smoother" and "more continuous" would've been better….

interesting to watch but can't see the point

The forkin' branches?

The way to defeat this type of hydra imo is to constantly choose to cut off the head that will cause the most growth. Eventually the base necks will not be able to either support the weight or the heart will give out trying to supply blood

Edit. Idea is from OOTS

Can you defeat a hydra that has infinite heads and regenerates infinite more if you cut one head?

Stab the body

Instead of Omega Squared, what about Omegamega XD

Instead of Omega to Omega, what about OmegatoMega

11,438,396,221,494 / 1.14e+13 / 11.4 Trillion steps to kill 4-head stack hydra

7,625,597,484,987 / 7.62e+12 / 7.6 Trillion heads in the spiky ball

why couldent they give us a better looking hydra i was just watching a warrhamer cinematic

Thats cheating

it looks like a tree (programmers will know what I'm talking about)

And I’ll form

The Head!

This channel needs to come back.

Make.it.happen.

Do not boast of mathematics as a solution.

When mathematics neutralizes one (hydra) to zero, it does so based on a logic of finite operational symmetric parity by technical limitation, not as you claim … but know that there is a natural numerical violation of parity, and it is not intuitively (Neutrins) generate exporadically couplings of that countable neutrality in zero, and transform them into neutrinos with charge and leave the confinement in the good sense of the word go out … as the light that creates and does not destroy.

Genesis 1: 4

And God separated the light from the darkness.

this seems a lot like weak and strong goodstein sequences

I always like this problem it relies on strictly decreasing set of ordinals eventually goes to zero …kind of like in calculus bounded monotonic decreasing sequences converge. The cool part is the realization of assigning the ordinals in such away you get this effect. Had to comment on it. Another aspect and more challenging problem to it…is trying to find the minimal amount of cuts to defeat it or how many cuts in general to defeat it for a given configuration… because counting of the ordinals in the chain is very difficult to count them all.

That makes it easier to kill doesnt it?

chop off heads till the hydra has too many heads and bodymass in relation to stomach and intenstinal capacity to feed it self sufficiently. Kill it with patience 😛

Try the body

No

each time a head is chopped off, that head is destroyed, and the copy of its branch is moved down, bringing it closer to the bottom.

This should be a video game lmao

Easier: stab its heart

Just stab it in the heart…..

10:20 What about if it grows ω new heads?

what about growing w heads after a chop?

Why can we encode a hydra's complexity using infinite ordinals?

Is this a joke?

How to kill the Hydra? Target the body, preferably a vital organ. Or just use a bomb!

I wanna sleep with this girl , hell yeah I want that !!!

3*omega=omega but omega*3 is not

She is so cute! (:

This paper defines such game between Hercules and Hydra.

It shows by this game that Goodstein’s Theorem is not provable using the Peano axioms of arithmetic.

https://faculty.baruch.cuny.edu/lkirby/accessible_independence_results.pdf

Dynamo will kill you with a head shot with awm

only an abstract mathematician can say nothing really changes when you increase the number of segments regrowing 🙂

Why don't you just chop off all of the heads touching the body? If we chop them off there will no longer be heads below it and so the hydra can't regrow them. It doesn't matter how many heads are stacked on one another. If you chop off the base every head or stack of heads stacked on it won't be able to regrow and if you do it for all "baseheads"(The closest heads to the body.) you

have basically defeated the hydra.

I think you can also use prime numbers to make orders. I think this is used in cryptography … or in Goedel's theorem? I'm not quite sure…

But in any case you can multiply any number of prime numbers with each other, and you can always trace back from the product which prime numbers it was built from.

Couldn't one use prime numbers as cardinals? And if so, why use these omega-cradinals anyway? What is the advantage?

_

[Translated from german to english with www.DeepL.com/Translator]

maybe we should just let it be

At 9:49 the picture is wrong it should have less head in the stack, they are showing a picture of w^w^3 not w^3

I cast Meteor Swarm

9:49 ain't it omega^(omega^3)?

I mean the branche are all 0.

next one is omega^0+omega^0+omega^0=1+1+1=3

next one omega^3

and the final one omega^(omega^3).

which makes sense since it is 2 more branches out there, so instead of

omega^(omega^1), it's now omega^(omega^3).

or did I get you wrong there?

I got 243 heads in the ball and 374 chops total for the bonus question. A length four will produce 9 length 3s in 5 moves and each length 3 takes 41 chops to kill. Similarly there are 9 3 length which will each turn into 27 heads, so 9*27 is 243 heads in ball.

(Yes, 2 years later, ikr)

Well, I guess I have figured it out.

Let A(H) be a function that returns number of heads attached to a body for a hydra described by H.

Also, to speak in general, let N be numbers of segments that regrow.

Now, if there are some heads growing from the one attached to the body, the hydra can be described by w^H.

We can notice, that basically, we want to reduce H to some number, and we'll get a ball of heads sticked to one.

We can tell from definition, that there are A(H) of this heads. So we got a hydra that is described by w^A(H).

Now we shall set a formula for A(w^k), where k is a natural number.

Notice, that if we cut off a head of w^k, we get (N + 1) segments described by w^(k-1).

Then A(w^k) = A( (N + 1) * w^(k – 1) ). Since these segments are independent we can tell that :

A(w^k) = (N + 1)A(w^(k-1)).

By solving this recurrence we get :

A(w^k) = (N + 1)^k

Since in our case N = 2, A(w^k) = 3^k.

Now, we have this formula, let's use it.

Hydra of height 4 is described by w^w^w.

A(w^w^w) = A(w^A(w^w)) = A( w^A( w^A(w) ) ) = A(w^A(w^3)) = A(w^(3^3)) = A(w^27) = 3^27.

And that shall be the answer 😀

great now prove that the speed of light is not constant.

Except you completely redefined the definition of a hydra making the entire premise pointless… Seriously if we allow the redefinition of things then anyone can theoretically do anything with anything…

I can do it easily, ever heard of a little thing called explosives

Feel like it would make a fun app.

What if the hydra grew omega heads each time a head was cut off? I presume it's impossible at that point, right?

What if in grow omega to omega to omega to omega to omega to omega heads

The sequence is decresing yes. But I dont see what guarantees that itll eventually reach 0.

well good thing i brought my Vorpal sword with me

Hydra: Im gonna kill you

Me: no i will kill you… Eventually

…

laterMe: that only took 12 quintillion years

kill the hyrda who regearates the part you killed and duplicate it (if it's finite)

Stab it in the heart

What about stabbing the body?

But what if it can regrow heads fom te body too?

Wow, math makes even killing a hydra boring

Haha, easy.

JUST STAB IT MULTIPLE TIMES. IT'LL DIE THAT WAY.Id cut of the bottom

Just stab the heart

I just jerked off, and this is the video I'm watching as I lay down to take a nap. This girl is making me wish this was the video I watched when I blew my load.

Don’t need to be a mythical hero or mathematician, just need loads of explosives.

or

you can chop off the main neck so all the heads fall on the ground and die

What happens if the hydra grows w (omega) heads every chop?

Will we be able to chop it all off (with an infinite number of chops)? Will it reach some steady state (meaning the number of heads doesn't change)?

Im not a mathmatitian, so yeah.

booooo

Divide by 0

Always use 0 if you're trying to slain infinite numbers.

better solution: put it in a box and put the box in a river and hurl the river at the sun and throw the sun into a blackhole. very simple

Just cut off so many heads that it starves to death from having to regenerate them all.

Imagine if Vsause made this video?

Literally

https://chrome.google.com/webstore/detail/threelly-ai-for-youtube/dfohlnjmjiipcppekkbhbabjbnikkibo

Lmao just shoot it

u can also cop off the connecting head to the body wich way all the heads are gone instandly

Plot twist: The hydra was a tree that was cursed.

Leave the poor animals alone!! They haven't hurt us so we shouldn't kill or even hurt them!!

Just imagine that each time it regenerates TREE(n) copies of its body after n-th cut

So is Aleph used as the cardinal of infinities?

Thought it said alchemical hydra from old school RuneScape , my bad

9:44 there is an error !!!!

Try to to make it regrow so many head that it will not be able to move and the hard will not be able to pump blood

What if it grows an ever increasingly increasing infinity of heads?