“any procedure or system of calculating it”

And any machine’s solution needs to be verified by a human for correctness. I am not talking about “how a machine would parse this equation”. I am talking about how humans have solved this for the last couple hundred years. Not sure how this will turn out on this forum, but let’s try:

Intro to Real Analysis by Bartle and Sherbert:

—————-QUOTE——-

X :=

1

— : n ∈ ℕ

2n

or more simply: X = 1/2n

———-End Quote———

You can verify that passage by googling the eBook.

The introduction to machines and programs have very much clouded the way things have been done historically. Wolfram|Alpha changed its code in 2013 and was solving it as above, before the change.

One of your arguments relies on : 2(2+1) = 2 x (2+1)

But doesn’t 2(2+1) also equal (2x(2+1)) ??

This is why the equation is ambiguous.

Since you also used machines as an argument, I strongly welcome your comment the following: Use wolfram|alpha and type in:

First example: cos2a

Second: cos2a/cos2a

Third: cos2a/b/cos2a/b

You can also find examples of algebraic division on a mathematician’s math page at Syracuse University:

http://cstl.syr.edu/fipse/algebra/unit2/parenth.htm

Eg: 6 / 2n = 3/n

Now let n=2+1 and solve both sides…

Remeber how we were taught to simplify algebraic division?

1 – Divide the coefficients of the like terms

2 – Subtraction the powers (exponents) of the like terms

Eg: 4a^2 / 2a = ??

Divide coefficients: 4 / 2 = 2

Subtract powers: 2-1 = 1

result: 2a

I stand by 1 as how I would solve it and how my colleagues would accept and understand it, however, after researching the topic, it is very clear how ambiguous it is :)

I look forward to your comments on these points.

King Regards,

your beloved mathman :)

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]]>Your explanation from the point view of 6/6 overlooked one math rule; Introduction of parenthesis or bracket.

While 6/(2(2+1)) = 1,

6/2(+1) = 9.

What helps our communications in math is the parenthesis or bracket.

6/6 = 6/(4+2) = 6/(2(2+1))! Here, as a math student one knows that the 2(2+1) is one as a denominator. However,

6/2(2+1) = 6/2x(2+1), which when either BODMAS or PEMDAS with LEFT TO RIGHT is applied you’ll get 9.

6/2x(3) = 3×3=9..

Now consider, 1/2n was shown in your comment.

This could be interpreted as (1/2) x n or 1 /(2n)

You’ll agree with me that both would give different answers. But in simple math operation, the expression if written the way it’s stated, i.e. 1/2n, any procedure or system of calculating it would take (1/2) x n. If the other is meant, it must surely be communicated with parenthesis or bracket, i.e. 1/(2n) any no mathematical method or procedure of calculation would mistake its answer.

Therefore beloved mathman, the expression 6/2(2+1) would simply be solved as 6/2*3=3*3=9.

Thank you.

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]]>.

6÷6=1..

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]]>This equation is 6 over 2(2+1).

No one ever wrote a / bc when they meant ac / b

That is because they are different expressions.

Distributive property cannot change the final value,

and, when used, is 6 / (4+2).

One more thing, do the factoring for 6 + 3 = 9

Now factor 6/2 from 6 + 3 and we get:

(6/2)2 + (6/2)1 = 9

Notice how 6/2 MUST be in parentheses?

Now final step:

(6/2)(2+1)

The same simple idea applies to “Foiling” binomials:

x+1(x+2) = x + ((1)x + (1)2)

(x+1)(x+2) = (x+1)x + (x+1)2

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]]>6/2*(1 + 2) = 9

6/2(1+2)= 1

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]]>6/2(1+2)=.?

first bracket

6/2(3)

again bracket

so want to solve the bracket..

2(3)=3

so,6/6

ie,,6/6=1

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]]>with respect to the notations, then I will address other points.

First,

if you want to say 0.5x, then you HAVE to write (1/2)x with parentheses or, x “all over 2″ with a horiztonal fraction bar, or write x/2. I have never

seen (1/2)x before I researched this equation, but since searching online, I HAVE seen fractional coefficients written this way, only because computers

are limited to the horizontal typing space.

Therefore:

x/2 = (1/2)x = 0.5x

1/2n = 1/(2n) This sort of notation is used especially with pi, ln, or e. We have never had to say 1/(2pi). It was simply 1/2pi, or 1/2e^2.

I have always used ab/cd to mean (ab)/(cd) and I topped almost all of my calculus classes since high school through university.(moot point, I know)

Just to re-iterate, to use 6/2 as a fraction, parentheses are REQUIRED. Every book will tell you this.

Now consider the Identity Law:

a = 1a = 1(a)

We know there is ALWAYS an ‘invisible’ 1 as a ceofficient of a variable if no other number is there. Therefore:

a/a = 1, and if a is also 1a, then a/1a = 1. Blindly using ‘pemdas’, some folks would do this:

a/1a = a/1*a = a*a = a^2. I hope this drives home the silliness of this calculation.

Now, on to my second point:

consider: factoring, simplifying equations, and the distributive property.

Lets start with the number 6.

6 = (4+2). There is a common factor here: 2. So let’s factor it out of both terms.

(4+2) = 2(2+1). The outside 2 remains a part of of the 2 inner terms at all times. It cannot be used in an operation by itself without the rest of (4+2).

The reverse of factoring is distribution, so, 2(2+1) = 6. This has to be true always. The argument I have seen to this is that (6/2) can be distributed.

This is true ONLY is 6/2 is in parentheses, otherwise, the 6 and 2 are separated by a division slash, and the 2 is a factor of 2+1.

So, let’s prove the initial equation:

6/6 = 1

6/(4+2) = 1

6/2(2+1) = 1

the same can be done for other factors:

6/6 = 1

6/(3+3) = 1

6/3(1+1) = 1

Distribution is actually a part of “Simplifying Equations” and is not bound to the order of operations as “multiplication”, since it is in fact “removing

parentheses by distributing”. This can be googled and several references found.

Simplifying 2(2+1) + 3(2+1) = 5(2+1). We “combined like terms” here, by adding, and did not perform the “parntheses” part of order of operations, nor did

we multiply, which is also higher priority than adding, because we only simplified.

Lastly, I hear the argument that “This is strictly numbers and you don’t use algebra rules since there are no variables”. That is the most asinine

arguement I have heard yet. All axioms, laws, and properties use variables, meaning that they hold true for “any number”, hence the proofs with

variables.

I welcome thoughts on this, in an intellectually formed response. I am tired of the ‘flaming’ that goes on by imbciles on some other forums with

rebuttals like “it is 9. go back to grade 3 you moron”, or “google says it is 9″, when google changes the equation to (6/2)*(2+1), and wolfram

contradicts itself with 2n/2n = 1, and 6/2n = 3/n, but then says 6/2(2+1) is 9. wolframs “terms” state that any answer should be verified with common

sense and accuracy should also be verified.

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]]>7 + (45/3) – (4*1) -2+5 =

7 + 15 – 4 -2+5 = 21

http://www.google.com/search?q=3%2B8-4%2B5*9%2F3-8%2F2*1-2%2B5

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]]>Wouldn’t this mean the difference between PEMDAS and BODMAS is the reason for different results? Thus PEMDAS can’t be commonly known as BODMAS in India. Instead, BODMAS is used instead of PEMDAS in India?

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]]>“Never assume malice when stupidity is equally applicable”

It is fairly basic stuff, but I’m not surprised a lot of people don’t remember it.

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]]>3+8-4+5*9/3-8/2*1-2+5 = ?

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]]>This is kiran i am new to SQL server and i need to list out all the tables used in stored procedure. collecting manually is very tedious job for such a long procedures so i am searching for alternative smart way. please suggest me how could i.

Thanks

Kiran

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