1 = -1 #shorts

In this video, I prove that 1 = -1 Did I really destroy all of math? Watch this video and find out!

[JSSTyger]

The real trick is that Dr. Peyam was simultaneously playing the harpsichord with his right hand.

[DrWeselcouch]

RIP math. 13 billlion BCE - 2/28/2021 CE

[yuvrajsinghjhala]

√(ab) = √a × √b, iff a and b are not both negative numbers.

[puerulus]

Since we're using the principal branch of the square root, we need -pi < arg(a) + arg(b) <= pi in order for the identity sqrt(ab) = sqrt(a)*sqrt(b) to hold.

[Vansh_Aggarwal_]

The problem is sqrt(ab)=sqrt(a).sqrt(b). If atleast one of (a, b) is positive. Since -1 is less than zero so 1 is not equal to i^2.

[gaster_]

You can use the formula sqrt(ab) = sqrt(a) x sqrt(b) only if a, b > 0. Here -1 is less than 0 so a, b < 0. Thus you cant use the formula here. That's how you got 1 = -1 :)

[harrywotton]

I think many people know what's wrong there, but the move of his writing is so cool.

[sumanmisra]

The solution:
Bodmas, if extended says that taking a root comes earlier than multiplication now this means that 1 ≠ √-1 * -1 since that becomes taking a root first so we apply identity getting i*i aka -1 so √1 actually breaks down as √(-1*[-1]) now it becomes 1=1 and not 1=-1 so step 3 is unjustified since expansion is wrong in step 2

[originmathematicsbyer.deep]

√(-1 )(-1)# √(-1) √(-1 )
. √ab =√a.√b if atleast one of a and b will be non negative

[thescienceguy]

If a and b are two negative numbers, then sqrt(ab) can't be written as sqrt(a) × sqrt(b)

That's all. 🤷🏻‍♂️

[alokdhardubey]

√(ab) = √a × √b iff a > 0 and b > 0
But yeah, this trick still looks cool 👍👍

[andreybyl]

the radical sign here denotes the root in the complex sense, so there is no error, since the square root is a two-valued function)))) and sqrt(1)={1, -1}

[hungryplate]

sqrt(ab)=sqrt(a)*sqrt(b) does not work for complex numbers.

[lolxdmekaisemaanlu]

Wrong.
You cannot write √(a.b) = √a.√b when 'a' and 'b' both are NEGATIVE.

[digvijaygadhavi]

The classic mistake done by 2 simulated technicians in Westworld Season 3 Episode 2 when Maeve asks one of the two technicians “I wonder if you’d be able to help me solve a little problem: what is the square root of negative one?”
"Well, negative one equals ‘i’ times ‘i’, " one responds.
"Which is the same as ‘the square root of negative one times the square root of negative one, '” adds the other.
"Negative one times negative one should be principal Square root of one."
Then the other says "but negative one and positive one can't be the same thing." Then both argues this again and again and then they got stuck in an infinite loop of argument and this helped her to add more complexity to break the whole simulation.

[elmaruchiha]

🤔 i thought the correct calcutation is:
√(-1)•√(-1) can be equal -i•i=1 .

[Alians]

More simplified, and definitely legit method:

1 = √1 = √(-1)^2 = -1

[anant_singh]

*sqrt [ (-a) (-b) ] = - sqrt (ab)*
The evil that lead to all the chaos 😂

[algorithminc.]

By the way ... maybe look for the channel "Boozetowne" with the video "7 into 28" ... old school math humor (Abbott & Costello). Also the channel "Steve Bass" with the video "Abbott & Costello: "Two Tens for a Five"" They enjoyed "breaking" math as much as we do. I mentioned your channel (in the comments) on the first one. Cheers ...

[HDitzzDH]

The mistake here I'm pretty sure is that the sqrt(x^2) is by definition the absolute value of x. So really we should have 1 = sqrt( i^2 ) = | i^2 | = |-1| = 1.