[noemon]

This guy in youtube has accumulated millions of views not only telling people to do something that is explicitly wrong based on his own statements but he also contradicts himself with his other videos where he proves why the rest of his videos are wrong. Confused? Just read on.

In this video:

He tells people not to remove the bracket even though the brackets/parentheses come first according to him!

In this video:

He tells people to make sure they wrap the 1/3 in parenthesis before they put it in a calculator because (1/3) is a single group and must not be ungrouped because if you insert into a calculator the expression 9-3/1/3+1 then the calculator will divide 3/1 first instead of 3/(1/3), which is absolutely correct advice, yet in the first video as well as his other video 6/2(1+2) he tells people to ungroup the group 2(1+2) and the group 2(2+2) so that he can divide 8/2 effectively first before he does anything else!

None of that registers with him as a contradiction and this person is supposed to be a Stanford Mathematician.

I find it astonishing how a mathematician from Stanford is unable to solve and provide proof for such a simple equation. I also find it breathtaking that they are unaware of the distributive property and also unaware that implied multiplication is so because it represents a single group. It is quite numbing that they are unaware that groups or parentheses take priority. 2a where a=2+2 is NOT Rocket Science, nor is it "ambiguous". Their provided "evidence" is a "calculator" or "google told me so". Is this what passes for PROOF in Stanford these days?

Even there they are wrong. All Scientific Calculators available in the market give the answer 1(one). See the 'How and Why of Mathematics' video where all calculators are compared 1 by 1, all the scientific calculators give the answer of 1 while all the toy-shop calculators give the answer 16. The same lady checking the calculators sends an email to CASIO asking them why did they change the order of operations in their non-scientifc range, and CASIO responds over an email which she publishes that an educator from the US contacted them and asked them to build such a stupid calculator. Somehow this is paraded as an alternative "modern convention". It's not, silly people are just silly and they do not represent something "modern", just their stupidity.

Bad software IS NOT an excuse for someone being unable to perform the simple task of order of operations, brackets first means the totallity of the bracket and not leaving it half-finished, 2(4) is still a bracket that needs to be removed by an OPERATION(hence order of OPERATIONS) and not by a "REWRITE"(which is NOT and OPERATION) to another DIFFERENT expression that magically breaks a group apart, so multiplying with its co-efficient is an OPERATION that removes the bracket before one can move to the division as per PEMDAS/GEMA; the same needs to happen via the distributive property nor is bad softare an excuse for being unable to solve an equation for x!

The author implicitly divides 8/2 first before he actually does anything else by default and no amount of nonsense changes the fact that they are wrong to divide before they do or finish the brackets first. The author simply takes the expression 8/2(2+2) and replaces it with another expression 4(2+2), which is not only not MATH, but it is just ad-hoc replacement of x with y or 1 with 9. It's just nonsense plain and simple.

However, I agree with them that this IS NOT AMBIGUOUS as some people claim it to be. He is just plainly wrong, unambiguously.

Here is REAL PROOF why 16 CANNOT be the answer as well as REAL PROOF why 1 is the ONLY Answer.

For 16 to be right in the equation 8/2(2+2)

2(2+2) must be 1/2

Or

2+2 must be 1/4

Let's Backtest

Assume 8/2(2+2) = 16

x = (2+2)

8/2x = 16

8 = 32x

x = 8/32

x = 1/4

Test if 1/4 = 2+2 = ERROR

Now assume 8/2(2+2) = 1

8/2x = 1

8=2x

x = 4

Test if 2+2 = 4 = CORRECT

----------

Do the same for 2(2+2)

Assume that 8/2(2+2) = 16

Replace 2(2+2) with x

Rewrite:

8/x=16
8/16=x
x=1/2

Test 1/2 = 2(2+2)=ERROR.

-------

Now assume that 8/2(2+2) = 1

We replace 2(2+2) with x

Rewrite:

8/x=1
x=8

Test 8 = 2(2+2) = CORRECT.

-----------------

2(2+2) can NEVER be 1/2.
2(2+2) is ALWAYS 8.
2+2 can NEVER be 1/4
2+2 is ALWAYS 4.

Therefore 8/2(2+2) = 1 and ONLY 1

There is no ambiguity in math or algebra nor is there a convention that says that division must be done before the parenthesis. That is just personal whims posturing as "modern practice" falsely.

In the other video: 9 - 3 ÷ (1/3) + 1

He gets it right, and right there he proves beyond doubt why all the other videos such as 6/2(1+2) and 8/2(2+2) are dead wrong.

In the 9 - 3 ÷ (1/3) + 1 video he tells people to group the 1/3 correctly when putting it into a calculator by adding parenthesis to it while in the first video he tells people to ungroup the groups 2(2+2) and 2(1+2) by removing their parentheses and rewriting something else such as 2*(2+2) for example which ungroups the group instead. He also tells people to do the division 8/2 before they do anything else and assume that the expression 8/2(2+2) is actually 4(2+2).

It's quite comical as no "convention" permits such a thing like doind the division before the parenthesis, groups or brackets.

He says "it is alarming that so many people get it wrong in Japan" yet he fails to spot the irony where he proactively tells people to get it wrong by failing to identify groups properly and then telling them to ungroup them.

Ironically the correct answer in the video 9 - 3 ÷ (1/3) + 1 is also 1(one).

I wrote the same post here.

If implied multiplication is used to define a single group then what about exponents why do they take priority in 2(3)^2?

Because the purpose of the superscript is identical to that of implied multiplication, to group a term even closer to another, even more so than implied multiplication does & hence its visually higher position and its name.

The only reason implied multiplication & superscripting exist is to group things together so that authors can omit what can be omitted and skip the use of extra parentheses and words due to laziness to minimize unrequired extra characters & also minimize the cost of printing [extra characters] too. It costs time, energy & money, so money cubed.

And hence why the exponent is superscripted at the top to denote its higher priority while maintaining a term bare of even more characters.

There is no other purpose of existence for either implied multiplication or the superscript or any type of math notation for that matter.

If a mathematician intends to write 1/2x where => (1/2)x, the same person can instead write x/2. We [humans] naturally fall back to the lowest common denominator in terms of omission.

That is the only reason for omission in the first place, hence 1/2x can never be intended to be x/2, because it would have been x/2 if that was intended given that x/2 contains even less characters. As such it can only be 1 divided by 2x because that is the minimum amount of characters that may be used to express something consistently using said notation.

Notation serves a single purpose alone to allow us to omit stuff(the only such stuff being extra parentheses for groupings and natural language in the more general sense) just so we can maintain consistent understanding by way of comprehending the notational baseline.

This has escaped people who have mangled things so much that they now fail to understand the raison d' etre of implied notation such as superscripting and implied multiplication as well as math notation more generally.

They will baffle future generations both in terms of pupils and archeologists too.

They effectively take a notational system intended to minimise characters and break its purpose while mutating it to a system that no longer cares about doing the very thing it is supposed to be doing.

If the argument is that we need to obey and transform our human visual programming based on lazy coding for some inexplicable reason we would also be obeying 9+2x3=33 instead of 15.