Yes, but more to the point it’s adults who’ve forgotten the rules. Students don’t have any issue with this. Exact same applies to all the order of operations memes floating around, like 6/2(1+2) - students have no trouble with it, it’s adults who’ve forgotten the rules who argue about it.
Nope, you can’t assume the - is included in the square if there’s no parenthesis around it. The answer is -9. Think of it like “0-3²” which is more obviously -9.
Nope, you can’t assume the - is included in the square if there’s no parenthesis around it. The answer is -9.
Surely that would mean the answer’s ambiguous, no? The lack of brackets means we can’t know definitively if - is included or not. But separately, I’d argue that -3 represents negative three, not subtract three, and negative three is it’s own distinct number from positive three.
Surely that would mean the answer’s ambiguous, no?
No. Exponents before Subtraction. Order of operations rules.
The lack of brackets means we can’t know definitively if - is included or not
The lack of brackets mean we definitively do know that it’s not included, because to be included, it would have to be in brackets.
I’d argue that -3 represents negative three, not subtract three
It’s actually 0-3. There’s an unwritten 0, just like if the first number was positive there’s an unwritten +. 9 is actually 0+9. All operations on the number line start from 0.
negative three is it’s own distinct number from positive three
Perhaps it’s not the most clear, but that absolutely is the standard convention for how to treat exponents, because it results in much simpler shorthand for writing things like this:
It’s been a hot minute since I’ve had to do any serious maths, but that does roughly line up with what I remember about BODMAS. It’s just intuitively, there’s a difference between - as an infix operator (10 - 5) and - as a prefix (-3). If you where to solve x2 where x = -3, I don’t think you’d say it’s -9.
there’s a difference between - as an infix operator (10 - 5) and - as a prefix (-3).
The only difference is whether it’s in brackets or not. To square the number -3 you need to put it in brackets, otherwise you’re only squaring 3.
x2 where x = -3, I don’t think you’d say it’s -9
That’s because anytime you substitute for a pronumeral, whatever the pronumeral represents goes in brackets. e.g. for x=3, 2x=2(3). So if x=-3, then x²=(-3)², as opposed to if x=3, we have -x²=-(3)². Whatever the pronumeral is equal to is inside brackets when you substitute.
There’s no multiplication, just subtraction (from an unwritten 0). -3² = 0-3²
there is no space to indicate the - represents a subtraction operator
Spaces don’t mean anything in Maths, and I don’t know why people keep adding them in! A minus sign is a minus sign, whether there are spaces next to it or not.
the immediate prefix - actually represents: (-1)x
No, it actually doesn’t. It represents 0-x. Every operation on the number line starts from 0.
this actually represents (-1)(x²)
No, it actually represents 0-x²
such that PEMDAS is upheld
Which what you wrote doesn’t. M refers literally to Multiplication signs. S refers literally to subtraction signs. -x² is E then S in PEMDAS.
I don’t make these rules
You did make those up actually (or you’ve repeated someone else who made them up).
but this is how it works
No it isn’t. A minus sign is the S in PEMDAS, not M.
Double check in wolfram alpha if you doubt it
Look in a Maths textbook. Wolfram is known to be wrong in several areas. University professors warn their students against using it without adding brackets everywhere.
It’s -(3^2) that’s the rule right??
Correct, or, -1 x 3^2 Joke is democracy doesn’t always get it right
Yes, but more to the point it’s adults who’ve forgotten the rules. Students don’t have any issue with this. Exact same applies to all the order of operations memes floating around, like 6/2(1+2) - students have no trouble with it, it’s adults who’ve forgotten the rules who argue about it.
I would say it’s -3 × -3.
Nope, you can’t assume the - is included in the square if there’s no parenthesis around it. The answer is -9. Think of it like “0-3²” which is more obviously -9.
Surely that would mean the answer’s ambiguous, no? The lack of brackets means we can’t know definitively if - is included or not. But separately, I’d argue that -3 represents negative three, not subtract three, and negative three is it’s own distinct number from positive three.
No. Exponents before Subtraction. Order of operations rules.
The lack of brackets mean we definitively do know that it’s not included, because to be included, it would have to be in brackets.
It’s actually 0-3. There’s an unwritten 0, just like if the first number was positive there’s an unwritten +. 9 is actually 0+9. All operations on the number line start from 0.
“positive 3” is actually 0+3.
Perhaps it’s not the most clear, but that absolutely is the standard convention for how to treat exponents, because it results in much simpler shorthand for writing things like this:
https://en.wikipedia.org/wiki/Taylor_series
Example on that page:
-x-(1/2)x^2 -(1/3)x^3 -(1/4)x^4 …
Using your definition you’d have to put a bunch of parenthesis: -x-(1/2)(x^2 )-(1/3)(x^3 )-(1/4)(x^4 )…
And believe me physicists would hate you if you made them do this because they’d have to do it constantly.
It’s been a hot minute since I’ve had to do any serious maths, but that does roughly line up with what I remember about BODMAS. It’s just intuitively, there’s a difference between - as an infix operator (10 - 5) and - as a prefix (-3). If you where to solve x2 where x = -3, I don’t think you’d say it’s -9.
The only difference is whether it’s in brackets or not. To square the number -3 you need to put it in brackets, otherwise you’re only squaring 3.
That’s because anytime you substitute for a pronumeral, whatever the pronumeral represents goes in brackets. e.g. for x=3, 2x=2(3). So if x=-3, then x²=(-3)², as opposed to if x=3, we have -x²=-(3)². Whatever the pronumeral is equal to is inside brackets when you substitute.
No, PEMDAS.
You do the exponent first, then multiplication.
-3² = -1 * 3²
or
-3² = (-1)(3²)
(-3)² would be how you’d represent what you are interpreting it as.
Your interpretation:
-3² != (-3)² = (-1(3))² = (-1 * 3)² = 9
vs
Correct Interpretation:
-3² = -3² = (-1)(3²) = -1 * 3² = -9
EDIT:
Every time you see a - directly infront of a number, say…
-x
…and there is no space to indicate the - represents a subtraction operator, such as in…
y - x
…the immediate prefix - actually represents:
(-1)x
or
-1 * x
Due to PEMDAS, if the exponent ² or ^2 is attached to…
-x² or -x^2
… this actually represents
(-1)(x²) or -1 * x^2
… such that PEMDAS is upheld, and the exponent recieves computational primacy.
EDIT 2:
I don’t make these rules, but this is how it works.
Double check in wolfram alpha if you doubt it.
There’s no multiplication, just subtraction (from an unwritten 0). -3² = 0-3²
Spaces don’t mean anything in Maths, and I don’t know why people keep adding them in! A minus sign is a minus sign, whether there are spaces next to it or not.
No, it actually doesn’t. It represents 0-x. Every operation on the number line starts from 0.
No, it actually represents 0-x²
Which what you wrote doesn’t. M refers literally to Multiplication signs. S refers literally to subtraction signs. -x² is E then S in PEMDAS.
You did make those up actually (or you’ve repeated someone else who made them up).
No it isn’t. A minus sign is the S in PEMDAS, not M.
Look in a Maths textbook. Wolfram is known to be wrong in several areas. University professors warn their students against using it without adding brackets everywhere.
Well, in my defense, that’s has the uglies.
Well, the alternative is to have to write -(3)² every time to show it’s not (-3)², so pick your poison.