False proof 2 + 2 = 5. Can you spot the mistake?

[@navghtivs]

80% of such proofs are division by zero; 10% are flipping around square root (case here); 5% summing divergent series.

[@merlinkestrel7716]

I think there are 5% missing there brotha

[@Prof-Joe-H]

@@merlinkestrel7716 Rightly so: The remaining 5% are about messing around with percentages. 😉

[@asdfqwerty14587]

@@merlinkestrel7716 There are lots of weird ways to create these kinds of false proofs, a full list of them would be excessively long.

[@scarletevans4474]

I petition for extra 5% for false proofs using complex numbers, like: e^(2i𝜋) = 1 = sqrt(1) = sqrt(e^(2i𝜋)) = e^(2i𝜋/2) = e^(i𝜋) = -1 Thus, 1 = -1.

[@sanamite]

​​@@merlinkestrel7716It's not exhaustive, that would take years to find all the similar proofs ever made (ok maybe more than years, and probably impossible)

[@j.n.-fr5uh]

the mistake is the part where it says 2+2=5

[@Navieddamooc]

I am the mistake

[@volodyanarchist]

Then this proves that 2+2 4

[@Navieddamooc]

@@volodyanarchist yesir

[@farhanrejwan]

what basically happened here is, by assuming -1/2 = 1/2, they 'proved' that from 2+2=4 we can get 2+2=5.

[@johnjeffreys6440]

Ya, it's not really a mistake, it's just false.

[@9adam4]

"Let's start at the bottom, because the mistake is at the top and I want a longer video."

[@FredThe-d1q]

Yeah, it's the first step that's so obviously wrong.

[@Warcraft_Traveler]

@@FredThe-d1q Nothing wrong with the 1st step. You can add and substract the same number to anything and you end up with the same result. The 2nd step however ...

[@FredThe-d1q]

@@Warcraft_Traveler Ok, 2nd step.

[@potatomudkip]

@@FredThe-d1qTo be fair, its technically correct in the same way that squares are technically rectangles. Yea, but conventionally no.

[@pettrovich]

My thoughts exactly

[@msdppdsm]

This proof goes something like this: 4 = 4-4.5+4.5 = |4-4.5| + 4.5 = |4.5-4| + 4.5 = 4.5-4+4.5= 5

[@Patrik6920]

the promplem is it ty to proove that -2 = √(-2)², √(-2)² = i√(2)² =i√4 = i2 ≠ -2

[@chriswebster24]

That’s a pretty big promplem, if you ax me.

[@grumpysanta6318]

Yes, it only works for very large values of 2.

[@1tubax]

🤣🤣

[@volodyanarchist]

Or even values of 5... except when it is 6.

[@simonmesserli7426]

😂😂😂😂😂😂

[@Vex-MTG]

This exactly. 2 is not 2.0

[@jssamp4442]

Perfect! Only when 2 >> 2.

[@OrangeDinoRBLX]

hear me out guys: if you put 2 and 2 together it’s 22. what’s the 22nd letter of the alphabet? V. What is that in Roman Numerals? 5. Point proven.

[@MasterTMO]

This answer is more valid...

[@mikeguilmette776]

Rocky V plus Rocky II equals . . . Rocky VII, Adrian's Revenge!

[@darksidegaming9806]

POV of an Engineer : 2 + 2 = 5 Cause, 2 = e => e = π => π = 3 ==> 2 + 2 = 2 + 3 = 5 Or More is better than getting in problem if the calculation is mistaken.

[@scarletevans4474]

e+e = 2e 2.something + 2.something = 5.something so approximately: 2 + 2 = 5

[@farhanrejwan]

@@scarletevans4474 math students back then : e + e = 2e math students now : e + e = eeeeeeeeeeeeeeee

[@BeastHighlightsOfficial]

2*infinity + 2*infinity = 5*infinity therefore 2+2=5

[@mikeguilmette776]

This reminds me of the electrical engineer who tried to tell me that the reciprocal of zero is infinity . . . because zero has an infinitesimal value. I asked him how many fires he's started.

[@yensteel]

I actually recently read about how NASA wasted $327 Million dollars for their mars space probe mission because their different departments were using the Metric and Imperial system simultaneously and assumed the other departments were aligned. So acceleration was way off and the probe crashed.

[@DanielWalvin]

The problem is simply that squaring is not an invertible function, "√(x²) = x" is only true for positive numbers and 0, not negative ones. So the error comes in already on the second line: 4 - 9/2 = -1/2, √((4 - 9/2)²) = √((-1/2)²) = √(1/4) = 1/2, -1/2 ≠ 1/2. Donezo.

[@MichaelPiz]

I'm going to use "donezo" instead of Q.E.D. from now on.

[@DanielWalvin]

​@@MichaelPizHeehee, love to hear it! XD

[@ryanbi]

❤😊

[@aristokatclaude3413]

Ah! now we have a proof for -1/2 = 1/2

[@Bill_W_Cipher]

What I do when I see these kinds of fake proofs is that I compute the value of each of these, and find when the value changes. Then I look at that step and direct all my attention to it and try to figure out why its wrong.

[@gavindeane3670]

Exactly. Once you've done that for a few of them, it becomes clear they tend to use the same fallacy. Divide by zero is a common one. Another common one, as here, is doing √(x²) = x with a negative value for x. Once you're used to the common errors it's easy to identify them.

[@foogod4237]

Easy: They're using square roots. Find the step where they're taking the square root of the square of a negative number. That's the mistake. That's _always_ the mistake. (as it happens, if you go top to bottom, it's the very first step that has a square root in it)

[@plonkster]

I didn't even see the number was negative. I just saw the square root of the squared term and immediately knew they are banking on having two roots.

[@logicplague]

Been a while since college, but isn't this where imaginary numbers come in? (oh, the irony)

[@steffenjensen422]

I kept looking for the part where they sneakily divide by zero and completely missed that they messed up the square root instead.

[@gavindeane3670]

​@@logicplagueNo. Imaginary numbers come in when you are taking the square root of a negative number. That's not what the "proof" is doing here. The "proof" is doing √(x²) with a negative value of x. Imaginary numbers come into it when you do √x with a negative value of x.

[@gavindeane3670]

Quite often the mistake in these "proofs" is dividing by zero.

[@bhaskar_yours]

My teachers taught me to never cross out square and square roots when you see them together. Here's what he taught me to do instead: f(x) = √(x²) = | x | which results in for example: f(1) = 1 which follows x = x as x is +ve f(-1) = 1 which follows x = - x as x is -ve

[@R00KIE_GUY]

As an engineer, 2+2 does equal 5. 2+2=4 plus 1 for safety, which gives us 5. ¯\_(ツ)_/¯

[@queefyg490]

Square root of square implies absolute value this means they add the 0.5 to 4.5 instead of subtracting. Step 2

[@m3tz-05]

2 + 2 = 5 Proof by Radiohead

[@balorprice]

I came to the comments section to ensure everyone's been paying attention, paying attention, paying attention

[@yeetusfetusdeletus]

i really want your comment to get to the top grrr

[@kenmore01]

My biggest wonder is why anyone would go through such a lengthy and time consuming process to prove something they know is not true.

[@wildgurgs3614]

For the meeeeeeeeeemes

[@extremecentrism9796]

Some people just want to watch the world burn

[@bjornfeuerbacher5514]

It's an elaborate form of trolling.

[@velisvideos6208]

Who says this isn't true? The Deep State is trying to force us believe that old 2+2 = 4 trope. No more! Probably George Soros is involved somehow.

[@trueriver1950]

To see if they can find a counter example. This would then make the whole of number theory inconsistent, but just think of the fame if you were the one to find it...

[@akashgarg5770]

in 1 line, all they did is replaced (4-9/2)^2 = (5-9/2)^2 i.e. (-0.5)^2 = (0.5)^2

[@marcusscience23]

I have an interesting story about square-root functions: When we were learning about quadratic functions in Math class, we were taught that a parabola could intersect the x-axis at 2 points, 1 point, or 0 points. When asked what happens with the y-axis, my Math teacher actually challenged us to make a parabola that didn’t cross the y-axis. I knew she didn’t expect any of us to get it, since any quadratic function y = ax^2 + b^x + c necessarily intersects the y-axis at (0 , c), so it will always intersect the y-axis once. But I quickly realized what she hasn’t: parabolas could be rotated. I graphed out x = y^2 + 1 , a rotated parabola that evidently did not cross the y-axis. It would have been some sort of a square-root function. After showing it to her, my teacher was confused at first, but admitted I had beaten the challenge. Later, when we were learning about functions, she showed my parabola to the class as an example of a graph which wasn’t a function (as it failed the vertical line test), and explained that it was actually two functions side-by-side: one with the positive square root of (x - 1) and the other with the negative square root of (x - 1). So, the point is that a square root graph is a relation, but not a function. However, it can be split into 2 separate functions, one with the positive square root and the other with the negative square root. You just need to make sure you know which one to use, so you can avoid errors like this false proof.

[@trueriver1950]

Square roots are sometimes described as a mapping rather than a relation. I'm personally unclear about whether that's saying the same thing or something subtly different but, ummmm, related

[@PoppySuzumi1223]

A positive number has a positive and a negative square root; the positive root is called the principal root (Absolute root |x|) , the negative root is called the imaginary root (Complex root ix). When you know that, everything's will be clearer to understand. e.g. √16 = +4 only, as the rule of principal root, i.e. √16 = |±4| = 4 But both 4 and - 4, when squaring them, both are 16 as it is what *Squaring* means.

[@Prof-Joe-H]

In between you are mixing up a negative root (-x) with an imaginary root (ix). The given problem is about the squaring of real numbers not being injective, which is intelligible in the real numbers domain without involving complex numbers. Yet, in the complex domain, there is a similar situation regarding the square root of a negative real number, where +ix and -ix (positive imaginary and negative imaginary) will be considered. 🤓

[@thomaslangbein297]

What have imaginary numbers got to do with negative numbers? You certainly mean the right thing, but you have to work on your argumentation line. Principal roots is a terminus of complex algebra. The (positive) sqr of a positive numbers is always positive (per definitionem). It’s as simple as that. And a square of any real number (unless 0) is positive.

[@Firelordthe64th]

This is positive number supremacy and lies told by big math

[@argoneum]

Absolute value extends to complex numbers as modulus. The absolute length of a vector, no matter the direction 😸

[@coreyyanofsky]

you can skip checking line by line for all the manipulations under the radical: at the top you have (-0.5)² and at the bottom you have (0.5)² and these are obviously equal

[@cookiesandcream7]

literally 1984

[@Warcraft_Traveler]

Mistake on the 3rd line. On the 2nd line, 4-9/2 makes -1/2. On the 3rd, because of the squareroot-squaring we end up with +1/2. 1/2-(-1/2)=1, so we have a difference of 1 with the original statement.

[@williamzeng464]

from 0:46 i can already see the problem; roots always have positive and negative answers, people are ignoring the negative one and using it as an absolute value function, which is wrong

[@abysslight2490]

The big takeaway from this is that while we think of square and square root as inverse operations, "cancelling the operation out" using function composition does not work both ways. Normally, for any function f(x), f(f⁻¹(x)) = x AND f⁻¹(f(x)) = x. However, for squares and square roots, this is not the case. if f(x) = x², and f⁻¹(x) = √x, f(f⁻¹(x)) = x, meaning (√x)² = x, but f⁻¹(f(x)) = |x|, meaning √x² = |x|, not just x. If you take the square root first, it works. If you square first, it only works if your number is positive. 4 - 9/2 is not positive.

[@thomaslangbein297]

That’s too easy. 4-9/2 is negative. The sqr of its square is positive. Magicians have to hide there tricks better.

[@Zorlig]

It's so nice of them to put the error in the very first (second?) line so it doesn't take much effort to solve.

[@Peter_1986]

Basically, the solution steps turned 4 - 9/2 into its absolute value.

[@GRACFUL1]

Don't let the math control you, you control the math.

[@Herby-1620]

The other trick is to divide by zero in some form of variable pair or some such.

[@aComedicPianist]

This is also why you should simplify on each step if you can, make the radical and power into a fractional exponent, and definitely simplify the fractional exponent, e.g. 2/2 = 1. You should also do the root first (after simplifying the fractional exponent) to prevent problems like this from arising.

[@mirandahotspring4019]

This is one of those, "Let's make the problem look so complicated no one will bother to check it." solutions.

[@robinlindgren6429]

the issue lies in taking the square root of the square of x and equating it to x. sqrt(x^2) is not x. it is the absolute value of x. 4-9/2 = -0.5 sqrt((4-9/2)^2) = 0.5 sqrt((5-9/2)^2) = 0.5 5-9/2 = 0.5

[@teelo12000]

Note that if we denote that we're taking the secondary (negative) root of the square root in the original proof, the end result becomes the expected 4.

[@abhirupkundu2778]

The biggest mistake in this problem is assuing square root returns negative values when it is clearly defined to be a one-one function with unique outputs(positive real numbers) when any thing is put as an input in its domain(positive numbers once again)

[@XxProGamerUSAxX]

"whatever stretches the video the furthest" -this man making the video

[@hkcprivate6977]

this was SO obvious and I'm at 0:45 and I figured it out. 4 - 4.5 is -0.5, but taking the square root of a squared number takes the abs so that's like saying -0.5 = 0.5

[@---Sasha---]

bro started from the bottom for more watch time, not mad at him tho

[@catakuri6678]

the mistake is the line that said: 2+2=4 because that's not what they're trying to prove

[@waulbrychi_schparku]

The third step is wrong (sqrt((4-9/2)²)+9/2) , bc sqrt of square is an absolute value

[@ThePowerfulOne07]

I’ve debated with people about taking the square root of a number squared. Gotta be careful!

[@kenmore01]

Cool party vibe!! 😁

[@trueriver1950]

sqrt ( x^2 ) simplifies to abs (x), for any real x, as by definition sqrt always returns the positive root This trick is used indirectly by electrical engineers when they calculate the RMS of a sine wave

[@susanarendas]

Why would you put this on KZbin? And going backwards to prove this is inaccurate and just a silly waste of time, and more thoroughly confusing to the student who is truly trying to learn. Find a better hobby!

[@VaresBonne]

7:54 why not use the bottom side of the equation then? why top side?

[@alanalvarado8896]

I’m pretty sure it’s bc the equation of the inverse function is x = sqrt(y), and if y was negative (if we used the bottom side of the equation), we would have imaginary numbers for x.

[@handanyldzhan9232]

Well, finding the square root of a square can lead to "wizardry" like that.

[@ai314159]

Alternatively, the second step makes the choice of the negative branch of the square root. Then we also have to take the negative branch in the penultimate step, getting 9/2 - 5 + 9/2 = 4.

[@sr6424]

One lesson here. When you solving an algebraic problem. It might be good to square both sides and apply the root later. You need to take the plus and minus roots. Then check the answers in the original equation!

[@Maths_Wonderland]

Where is the ending music? 🧐🧐🧐

[@Neodynium.the_permanent_magnet]

My guess is some royalties issue?

[@deadshot9982]

8:34 I don’t understand how the graph disproves anything. (-2)^2 = 4, 2^2 = 4, sqr(4) = +-2. It can’t get any simpler than that. Am I just supposed to believe that your method is right even though there’s no reason for mine to be wrong?

[@sicknerd2929]

I think the problem lies in the way square root is defined in lower classes. It is simply described as a number which when squared gives us the desired number But that is not how we use it during real calculations. We don't see x^2 = a and write x=sqrt(a). We write x=+-sqrt(a). Which means sqrt (a) alone does not cover all the values which when squared give a. It only refers to the positive value that when squared gives a. So the real definition of a square root should be: A **positive value** that when squared gives us the desired number. In this new light it is incorrect to write 4-9/2 as sqrt(4 -9/2) ^2 since sqrt(4-9/2) ^2 is not 4-9/2 but the positive quantity 9/2-4. Hope it helps

[@gavindeane3670]

The "proof" is using the √ symbol. √4 is not ±2. √4 is 2. ±√4 is ±2

[@ismailshtewi8560]

i spent so long on this hunting for a point where they hid a division by zero

[@Elleander1]

Spotted the mistake immediately, I feel pretty nice

[@cpsof]

Binary search is a lot more effective way to find the mistake. Compute the value in the middle and if it's 4, the mistake is later, and if it's 5, the mistake is earlier. Then you can repeat this for the upper or lower half and keep halving the search range until the mistake is found.

[@22dolls19]

"The mistake is that I did nothing wrong, no reason to be dragged inside minilove"

[@PeacefulCommunitee]

Well thats why Axioms and Postulates are there..❤

[@baxtermullins1842]

Star Wars quote:”It’s a trap!”

[@timschommer8548]

I see he took feedback on board from the last video that handled square roots. Apprciated. Also makes me giggle a little bit, because it is fun to see those things evolve.

[@ravikiranpalaparthi615]

√[4-(9/2)]² has the error. 4-(9/2) = 4-4.5 = -0.5, square root cannot be applied to negative numbers.

[@marxcarton3858]

Order of operations is allways the biggest mistake. Expanding a numerical value as if it is a quadratic then adding together the numerical value to get another value is like saying (x+2)^2 = x^2 + 4x + 4 and 4x+4=8☠☠

[@henke37]

My gut called it being a squaring negatives issue. And that the error was at the beginning.

[@joeschmo622]

2 + 2 = 5, for sufficiently large values of 2.

[@abcde_5949]

It's always the negative root trick

[@nonroutineganit7682]

√(4 - 9/2)² = | 4 - 9/2 | At the 2nd step you are wrong

[@bundzsi]

By definition sqrt(x^2) = |x| and not just x. This is where this proof fails

[@kaydenlimpert2779]

i looked through the proof and saw that 4-9/2 was negative which would mean you need a - at the beginning

[@dulcinealee3933]

Where did the 9 come from?

[@MaryMusat]

De sub radical de scoate in modul : 9/2-5+9/2=9-5=4

[@nychold]

4 - 9/2 is negative, so just pulling it into a radical is a violation even as a square, as it would require a negative number coming out of a square root, which is technically impossible.

[@aryangupta211]

At timestamp 5:15 You are wrong .... Because as you would explain later √(x *x) = x , sign will the decided by value of x. Here, although it is indeed √(1/4) but is actually √((-1/2)(-1/2)) hence, it will be (-1/2) and not (+1/2). The actual mistake lies in the second last line while factoring. Where a grouping of squared term is done the wrong way. For example, (a² - 2ab + b² ) = (a-b)² . But how can you so sure that it is not (b-a)² . There, the mistake is the same wrong interpretation of this additive identity.

[@josephwest124]

It's been many a year since I took a math class but my biggest question is "Where did the value of '-9/2 + 9/2' come from in the initial step?" Why not use "-16/9 + 16/9" or "-22/7 + 22/7" instead? I mean, simply inserting a "sum" of fractions to an equation is not something I recall from any of my algebra, geometry, trig or calculus classes. (I do remember the old "proof" of "2 + 2 = 5" by resorting to the mathematically illogical step of dividing by zero--it's been years and I don't recall the specifics of that "proof"--but, at least that "proof" didn't start off by adding extraneous material to the original equation.)

[@gavindeane3670]

There is absolutely nothing wrong with the 2+2 = 4-9/2+9/2 line. The problem is the next line.

[@fabiog627]

A function has only one value if you define it in the real domain, in the complex domain functions can have more than one value.

[@MonochromeWench]

Square root giving only the positive result would be why we explicitly use ± before the square root in the Quadratic formula. If Square root could give positive or negative the ± would not be needed.

[@MDPeetje]

Why does it have to remain a function when inversing it? I understand that this is the convention and i also only consider the positive square root when i see it like this. But in my opinion it would be much simpler to have the convention be considering both solutions and if you should only consider the negative or positive one then put a minus or plus sign above the root. Simply because y² = x isn't an function doesn't mean that there is only 1 solution for x but somehow for y = √x then there is only 1 solution? This choice for the convention has always seen to be an subjective choice to me instead of a logical/objective one.

[@franklee663]

The second step is already wrong, if you apply squares and sqrt, you cannot selective choose terms but have to apply to all on one side.

[@swoldoge]

No outtro music? 🥺

[@Rick_MacKenzie]

Would have been interesting to demonstrate that computation would be correct if you take the negative root of (4-9/2)^2 instead of the principle square root.

[@proboiz_50]

I knew it! My instincts told me at the start of the video that the 3rd line is incorrect

[@arnavthescientist1149]

Ok 4-(9/2) is negative hence it can't be squared and then square rooted. 0:47

[@PhilipMurphy8]

The smartest people would notice the mistake straight away

[@cmilkau]

These are really easy to spot if you calculate the intermediate results.

[@ShawnF6FHellcat]

I love math, but my most hated mathematical phrase is "prove it"...

[@YaztromoX]

My refutation of this “proof” is that you can’t start a proof with “2 + 2 = 4” and finish with “2 + 2 = 5”. If this “proof” didn’t _have_ a mistake, then at best all that was proven is that “2 + 2” is either non-computable, or that it satisfies every possible value (similar to the solution of “x - x = 0”). But you can’t posit that 2 + 2 = 4 as your starting point, come up with a ‘5’, and then state that it proves that “2 + 2 = 5”, as the result refutes your starting point.

[@onradioactivewaves]

He used large values of 2, the mistake was not stating that

[@YaztromoX]

@ - I get this is a joke, but the point is that all this proof proves is that there is a contradiction, and if not for the error it would simply show that the predicate they started with is wrong, and not that 2 + 2 = 5. Even for very large values of 2.

[@Cuber_Man1]

You basically took the absolute value of a negative number in the very first step. In others words, your saying that -0.5=0.5

[@PowerStar004]

(sqrt (4-(9/2)^2))+(9/2) = 5 The "mistake" is that by squaring and rooting everything EXCEPT the +(9/2) the value is changed.

[@pk2712]

When you go from = 4-9/2+ 9/2 to = sqrt((4-9/2)^2) +9/2 , there is an error because the assumption is made that 4-9/2= sqrt((4-9/2)^2) --- this is wrong . 4-9/2 = --1/2 , and sqrt((4-9/2)^2) = absolutevalueof(4-9/2)=1/2 .

[@TheSecondB-nn2vt]

-1/2≠sqrt((-1/2)^2 )

[@williamstraub3844]

A square root always has two roots, plus and minus, unless the number is zero or negative.

[@fillforked]

you can just check if it equals 4 and it doesnt. it equals root 4.75, what else is there to it?

[@sicknerd2929]

What happened to the outro music? Does anyone know?

[@AlejandroMira-r9v]

People that enjoy learning math / want to understand the gaps that are often left in school: Do you care about the historical context of why a math concept was created or began to be useful? Or do you care about how you can arrive to those same conclusions by your own means? Or other? Or all of them? I want to hear you :)

[@battlesheep2552]

4:45 well it's false because of the proof by contradiction we went over

[@tntdude999]

What I would do, is evaluate the value of every expression and the see which step it changes.

[@demise0]

Can generally figure it out by doing the math at each step. As soon as the square and square root went up in line 2, I saw a negative (4 - 9/2) = -1/2, suddenly become a positive 1/2 after squaring and (positive root) square rooting. Right there in step 2, the right side jumped from 4 to 5. The rest of the steps were all obfuscation.

[@jannegrey]

my guess - either division by zero or using square roots in wrong way. But I didn't even look on the problem yet.

[@DrHenry1987]

When I hear "convention", I always ask "according to who?". Where is this codified? We have those in chemistry too, and I irritate when asking the same questions, although some are now studying some "conventions" for their appropriateness.

[@Stevothehuman]

A false proof straight from Room 101

[@ChristofAbsolution]

Damn. I thought the problem happened when they added 2 + 3 on accident.

[@blablablabla4418]

Sqrt((4 - 9/2)^2) is .5 when it should be -0.5. Ez spot.

[@MrJavierSC1]

After the second line, which is incorrect since that radical represents the absolute value, you get 1/2 + 9/2 = 5. All the other steps seem unnecessary and likely aim to create confusion. Kind of sad these things get viral.

[@applerd209]

Sqrt(x^2)=abs(x)

[@treush8471]

In fact when you say that a number is the squareroot of itself always check that it is positive (common mistake)

[@bobbyheffley4955]

The mistake is taking the wrong sign of the square root.

[@devedrakumarvshah9288]

Sqrt of a number can be + or -. So the last step should have been 9/2 -5 +9/2 = 4

[@randomthings1325]

remember peps: "messing with powers like that is sus (sometimes)"

[@Thrillzrobloxbedwars]

The only problem is the second line says 2+2=4 then uses that to prove that its 5 which is not logically consistent as 2+2 cant be both 4 and 5 it has to have one answer.