Every Important Math Constant Explained 

That's actually really cool

I heard he was only using vowels, and he used a already

While the name "e" did not come from Euler's name, the name "Euler's number" certainly did.

🤓🤓🤓🤓

@@isavenewspapers8890 Nah, Euler just asked a random name generator to come up with a good name for this number and it popped out "Euler" by sheer coincidence.

not a big deal dude 🙃🙃

AI is not good at proper nouns. Also note the weird way is says "Pythagoras."

That's cause everyone loves Rayman

also Fibonaki? 😂

AI is reading it..

Fr?😅

@@Weskool1 It's a very special number and pops up everywhere in math, has a lot of interesting properties too

Ok but π=3 e=3 π=e e=2 2=√2 √2=1 sin(x)=x cos(x)=1 ∫f(x)dx=c i≈1

nah bro 0 clears

What a chad.

Many of the names of things were a bit fishy.

Not quite. We *think* that this is true, but we don’t know, we can’t prove it.

Yeah I was thinking the same thing. a^x is O(x^∞). Or, more precisely, lim h→0 (1+hx)^(1/h), making it O(x^(1/h)) in the limiting case as h→0, or O(x^w) in the limiting case as w→∞. If it was closed under even the most rapidly increasing elementary functions, there'd be no practical way to generate aleph 1.

@@kvOdratui you can quite easily prove that 2 ^ Aleph null > Aleph null, since you can find a bijection between a set of size 2 ^ Aleph null and a set of the cardinality of the real numbers

​@@kvOdratuiNo, it is definitely known that 2^Aleph0 > Aleph0 (by Cantor's theorem). What we do not know (and in a certain sense cannot know) is whether 2^Aleph0 = Aleph1 (continuum hypothesis).

there is too many Alehp Nulls to understand this

what

Wrong. Aleph_0 is the cardinality of the natural numbers. According to Cantor, the continuum is the power set of Aleph_0, or 2^(Aleph_0).

6:50 Yeah I did a double take when I heard that line too! I was like “WTF dude? 3 is not a variable! It’s a fixed value, and that value is fixed at 3.”

Agreed

Ikr

Hmmmm, I thought it was named π because the first letter of the word describing it is π.

Don’t forget he said “pie-the-gore-ass” 💀

Thanks for the idea!

Yup! It's because every non-integer rational is also not an integer when squared. This is because when a rational is not an integer, that means the denominator has something in its prime factorization that the numerator doesn't, and this doesn't change when squaring, as squaring just adds another copy to the prime factorization of both the numerator and denominator

💀

Same

⁠@@andrewsauer2729Wow that’s actually really cool! How have I never heard of this

@andrewsaur2729 Thanks for that really clean explanation. I had a little bit of an intuition for that fact that squaring decimal numbers doesn't create integers yesterday. But I'm still astounded by that fact. It seems like something that should have come up in a math class at some point. Like I always thought it was crazy that the square root of two is irrational and right under my nose are all these other irrational square roots.

it sounds too stretched out to be a smoke detector

i want to but its hard to reach and im kinda lazy 🦥 😂

LOL i didn’t notice that

Can you collaborate with me to make videos better? If interested, send me an email 📨

@@ThoughtThrill365 Is there money involved?

yes, pls send me an email, we will discuss.

@@ThoughtThrill365 What's your email address?

@@ThoughtThrill365Okay, what's your "mailbox", if you know what I'm saying? (RU-vid is being ridiculous right now.)

it's the opposite, i actively tried to correctly pronounce.

Every? Impossible. The most notable ones , yes , but it would still take a long time.

did you drank cocaine?

We don't know, maybe. n^aleph 0 ≥ aleph 1

@@nzqarc technically, we cannot say whether 2^aleph zero = aleph zero, because that is the continuum hypothesis which is undecidable (neither true nor false) in ZFC

That is what I remember. I believe the book was Asimov on Numbers from a long time ago. But maybe we learned more in the last 40+ years!

​@@nzqarc we do know, it's whatever we choose it to be. Both options, where it does equal aleph 1 and where it doesn't equal aleph 1, can be consistent, so both can be correct and we can choose the one we want. Like the statement "x³=1 has exactly one solution". We can let it be true, or false, and both work, but we have to live with the consequences. The consequences of making it true is that we must not have complex numbers, and making it false means we must have complex numbers.

It is a constant because it is a specific number with a specific (albeit imaginary) value. 3i, 4i, etc are also their own numbers. It is just like the imaginary version of "1". Sometimes it is called the imaginary unit, which is maybe more in line with what you are thinking. But it is not a variable.

No, the definition of irrational numbers is the exact opposite of that.

Eh, probably only a couple. I don't think he missed too much by leaving them out.

@@General12th wait but omg he also forgot 0, -1, -2, and maybe a few more in that direction

no well first of all it's unknown whether pi is normal (for all we know it could devolve into 010010001000000100000000001 or whatever) secondly no because 0% probabilistic chance

True :3

It isn't named BY Euler? No, he certainly did name the number "e". If you mean it isn't named AFTER Euler, that's also wrong, since we commonly call it "Euler's number".

@@isavenewspapers8890 Well I think what he meant is that it wasn't called "e" in honor of Euler. Obviously. And that is true.

Eulers number is just e

The perimeter of a circle is its circumference.

These are exactly the same

this is kinda bogus unless you rigorously define "closeness"

It's a number, for sure.

​@@isavenewspapers8890 I agree

It isn't really a famous constant, it is just an interesting possible solution to certain infinite series. But it's not like it had to be "discovered" as with most of the constants here.

Yes sir

It is defined, but it's not single valued.

“Aleph Null”

It is a ratio of two quantities, but one of those quantities is not an integer. To be rational it would need to be a ratio of two integers

It needs to be a ratio of integers, for any given circle if the diameter is an integer, the circumference will be irrational, and vice versa, so their ratio will never be a rational number

Every number x can be written as a ratio, like x/1. But rational means we can do it with integers specifically.

Bruh what

And Mathematics and Physicists chose the opposite values, so j=-i. (this is a joke)

i is distinguished from -i in complex numbers very clearly, isn't it? 3+4i and 3-4i aren't the same. Even if you just look at the imaginary number line, like on an Argand plane, obviously -i is just the negative of i, exactly like with real numbers. i-i is also 0, for example.

​@@HuckleberryHim you misunderstand. Consider the set {i,-i} and select a random ι in that set. Then write some expressions that use i, but replace each i with ι. You won't be able to tell which one you chose. They're functionally identical. sin(z)=(e^(ιz)-e^(-ιz))/(2ι) e^(πι)=-1 ι²=-1 e^(πι/2)=ι ι+(-ι)=0 ι(-ι)=1 lim(z→∞) sec(ι|z|)=0 sin(ιz)=ιsinh(z) Et cetera, et cetera. If you called -i=j and redrew the argand diagram with this in mind, nothing would change. The only reason we know i and -i are not the same is that they add to 0, but are not themselves 0 because they multiply to 1. This is why there's no ordering in the complex plane. i>0 is false, as is i

The dimensionless constants in physics aren't always so relatively nicely close to small integers. The fine structure constant is approximately 1/137, while the difference between the predicted vacuum energy and the observed vacuum energy is roughly 10^120. Planck units might be 0 or 1 naturally, but in our system of measurements, their magnitudes can be even more wild. Still, you're right that a lot of numbers in math and science are either integers close to 0 or relatively simple fractions (like 5/3 for turbulence). Is this because we build so much of our math off the simple numbers, so they always keep coming along for the ride? Or is there something fundamental about integers and rationals that's "intrinsic" to logic and the Universe themselves?

i factorial?!?

That means you use the number i, and you use the symbol i; you just don't use the latter for the former.

Why do you need imaginary numbers in electrical engineering?

I do coding, but we have something called fast fourier transform which is used in acoustics ​which i guess kinda relates to electrical engineering?? @lakshya4876