Dialogue de sourds about mathematics: Are exponents substractions in disguise?

[Hypersmurf]

I don't understand BEDMAS ...

Or do I?

What's it mean?

It's a mnemonic for remembering the order of operations - Brackets, Exponents, Division and Multiplication, Addition and Subtraction.

-Hyp.

 

[Patryn of Elvenshae]

It's a mnemonic for remembering the order of operations - Brackets, Exponents, Division and Multiplication, Addition and Subtraction.

Ah ... I learned it as "Please Excuse My Dumb-Ass Sister."

Parentheses
Exponents
Multiplication
Division
Addition
Subtraction

(Eventually with the understanding that E, M, and D were really the same step, and A and S were also the same step. Yay, Math!)

 

[Hypersmurf]

Eventually with the understanding that E, M, and D were really the same step...

Oh, dear.

So if I have the expression 2y², where y = 4...

... are you saying that 2(y²) and (2y)² are the same, since E and M happen at the same step in the process?

I'd much rather you had the understanding that E is a very distinct step from M and D, and happens first.

-Hyp.

 

[Saeviomagy]

Oh, dear.

So if I have the expression 2y², where y = 4...

... are you saying that 2(y²) and (2y)² are the same, since E and M happen at the same step in the process?

I'd much rather you had the understanding that E is a very distinct step from M and D, and happens first.

-Hyp.

2y^2 = 2*y*y

So E and M ARE the same step.

Your second example relies on parentheses, which we've established come first...

 

[Rystil Arden]

2y^2 = 2*y*y

So E and M ARE the same step.

Your second example relies on parentheses, which we've established come first...

When you compute 2y^2 = 2*y*y, you've violated your own incorrect order of operations. If exponents come at the same time as multiplication, then you would multiply 2 by y before doing the exponent.

Also, the logic in the 2y^2 = 2*y*y example could be used to attempt to prove that addition should come at the same time too, since you can simplify mulitiplication into a series of additions.

Finally, the comment about the parentheses in Hypersmurf's good example is begging the question. He put the parentheses there because he correctly recognised that they were necessary to show two different interpretations. If you beg the question and assume that you are right, then Hypersmurf's example becomes meaningless because the parentheses are not needed to indicate two interpretations.

 

[Patryn of Elvenshae]

When you compute 2y^2 = 2*y*y, you've violated your own incorrect order of operations. If exponents come at the same time as multiplication, then you would multiply 2 by y before doing the exponent.

No. An exponent is just shorthand for more multiplication. Nothing fancy about it.

 

[Rystil Arden]

No. An exponent is just shorthand for more multiplication. Nothing fancy about it.

Patryn: 2y^2 = 2*y*y is a correct statement, in that I'm sure we agree. But look above at Saev's order of operation. It is that which was violated, not the real order of operations. This is so because in expanding the exponent before calculating the multiplication to its left, he gave the exponent the preference it deserves. This would not be the case if exponents and multiplication came at the same time.

 

[ThirdWizard]

2(y²) = 2*y*y

(2y)² = 2y*2y

Very different outcomes, depending on if exponents come first or multiplication.

A similar example would be saying multiplication and addition come at the same time.

2y+2 = y+y+2

It doesn't mean

y+2+y+2 [as in 2(y+2)]

See?

 

[Thanee]

What Patryn said is, that you can cover Exponents and Multiplication in a single step, not Brackets and Exponents or Multiplication and Addition, just Exponents and Multiplication, since Exponents are just a shortcut for Multiplication.

Bye
Thanee

 

[ThirdWizard]

What Patryn said is, that you can cover Exponents and Multiplication in a single step, not Brackets and Exponents or Multiplication and Addition, just Exponents and Multiplication, since Exponents are just a shortcut for Multiplication.

Bye
Thanee

To which, we are disagreeing.

EDIT: to clarify, if exponents and multiplication were interchangable, then 2(y²) and (2y)² would be interchangable, much like 2(xy) and (2x)y are interchanable.