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.

[@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.

[@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

[@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

[@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

[@wernerviehhauser94]

wasn't it 25% safety factor?

[@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...

[@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

[@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.

[@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

[@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)

[@queefyg490]

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

[@R00KIE_GUY]

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

[@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

[@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.

[@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.

[@JohnDVil]

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 😸

[@cookiesandcream7]

literally 1984

[@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

[@thomaslangbein297]

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

[@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.

[@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

[@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.

[@bundzsi]

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

[@Herby-1620]

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

[@Peter_1986]

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

[@---Sasha---]

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

[@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

[@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.

[@GRACFUL1]

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

[@waulbrychi_schparku]

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

[@catakuri6678]

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

[@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)

[@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

[@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☠☠

[@joeschmo622]

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

[@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!

[@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.

[@abcde_5949]

It's always the negative root trick

[@mirandahotspring4019]

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

[@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

[@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

[@nonroutineganit7682]

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

[@PeacefulCommunitee]

Well thats why Axioms and Postulates are there..❤

[@Elleander1]

Spotted the mistake immediately, I feel pretty nice

[@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.

[@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.

[@handanyldzhan9232]

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

[@ismailshtewi8560]

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

[@Stevothehuman]

A false proof straight from Room 101

[@blablablabla4418]

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

[@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 )

[@henke37]

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

[@kaydenlimpert2779]

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

[@cuberdaboi2397]

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

[@22dolls19]

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

[@proboiz_50]

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

[@cmilkau]

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

[@bobbyheffley4955]

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

[@PhilipMurphy8]

The smartest people would notice the mistake straight away

[@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.

[@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.

[@andor6623]

Easiest thing I have done today

[@jannegrey]

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

[@ericerpelding686]

Terrence Howard should be informed about this proof!

[@Maths_Wonderland]

Where is the ending music? 🧐🧐🧐

[@Neodynium.the_permanent_magnet]

My guess is some royalties issue?

[@itsphoenixingtime]

POV of a Cosmologist 2 + 2 can be 5. It can be 10. It's probably about 100. Ok we'll just put it on the order of 10^0 - 10^1. Good enough.

[@NoProductionsGD]

there is no mistake, it's just floating point precision

[@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.

[@ShawnF6FHellcat]

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

[@tntdude999]

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

[@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.

[@rainerzufall42]

Early mistake: 4 - 9/2 is negative, -0.5. If you square it and take the square root, you only get the positive value +0.5. Add that to 9/2, and you get the respective values 4 and 5. End of story.

[@williamstraub3844]

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

[@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.

[@ChristofAbsolution]

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

[@romain.guillaume]

Well 2 seconds in and immediately I spotted the issue… the sqrt of a square is not the original number but it’s absolute value. So line 2 is false : 4 -9/2 being negative… In fact, evaluating the second line already gives 2+2=5…

[@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.

[@palpytine]

Multi values functions are a real thing very much recognised in mathematics. Perhaps nowhere more evident that in the roots of unity

[@balazslakatos9817]

interesting one, I was unable to find the problem.

[@okaro6595]

That is the problem with improper fractions. It is hard to see the magnitude. If they had used for example decimal 4.5 one would immediately notice it.

[@tolich3]

Ah, please. The moon is made of Swiss cheese, therefore 2+2=5. QED

[@arnavthescientist1149]

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

[@treush8471]

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

[@adrianandrews2254]

This is profoundly unsettling. A RULE is a convention - a choice. If I chose to not apply that rule then in my formulation - ie in MY maths - 4 DOES equal 5. While my maths may not be as useful as that using the RULE - IT IS EQUALLY VALID. The real mistake is that the conventions to be used are not stated when postulating the problem.

[@dividebyzero1000]

Agree with complaint about convention, but the mistake is clear. 1/2-1/2. All the nonsense about functions and conventions is for math majors and academic to argue about, not people who do real math at a practical/everyday level.

[@3dplanet100]

0:40 as soonest it says 2+2=4-9over2plus9over2 I didn't need further proof that the equation is false. 4 minus 9 over 2 plus 9 over 2 is 5 not 4. I don't know why many people falls for this.

[@denorangebanan]

what?

[@3dplanet100]

​@@denorangebananthat line 3 is -5 not 4. This is what I mean: 4.5 + 4.5 is 9. 4-9 is not 2+2 which is 4, but -5.

[@PrateekSrivastava789]

​@@3dplanet100 there are no brackets around 9/2+9/2 4 - 9/2 + 9/2 does not mean 4 - 9, it means 4 - 4.5 + 4.5 which is 4

[@arpitchauhan2147]

@3dplanet bro forget everyone u are doing great.... Don't listen to anyone and one day will be LITERALLY goat of maths

[@georgemathiellis5486]

spotted the negative value of the root at 50 seconds ....

[@divyanshbhatt5570]

The mistake is when we do not follow root(x^2)=modulus(x)

[@randomthings1325]

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

[@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.

[@truthdisseminator]

You could also have a function: y = -|x|

[@battlesheep2552]

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

[@wait_what_glitch]

I knew it from the beginning when i saw the first step

[@dinhnghiadan]

4x0=5x0 =>4=5🤔 quickly

[@movimentoamazonialivre9838]

Yes the square root of a quantity squared is plus or minus the quantity and in this case the minus sign was the correct one but is omitted from the proof.

[@ibrahimmalki150]

Am I the only one that thinks you just put a square root and square part of the equation so naturally there is a part that was ignored?

[@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.

[@DeepeshMaan]

the mistake is in the fact that (4-(9/2))^2 = (5-(9/2))^2 bcz (-0.5)^2 = (0.5)^2 but (4-(9/2)) not = (5-(9/2)) as (-0.5) not = (0.5)

[@gavindeane3670]

There's an immediate error on the second line. It's the √(x²) = x error. That is not true for negative x. That's one of the common errors in these silly "proofs". If it's not that then it's often a divide by zero, or sometimes it's doing √a • √b = √(ab) when a and b are negative.