Daughter's math homework (1 Viewer)

[Buckychudd]

There are negative numbers. Negative five, for example, is a negative number.

Yes, and if you square it, you get 25, not -25.

Exactly right. If you square negative five, you get 25.But in the expression -5^2, you are not squaring negative five.

In the expression 23^2, you are not squaring three.

The operation of the minus sign comes after the operation of the exponent. The operation of converting "23" into "(2*10 + 3*1) comes before the operation of the exponent.

This is not inconsistent or illogical. "2" and "3" are numerals, as is "5". "-" is not a numeral.

Converting paired numerals into a single value comes before any operators are applied.

Then operators are applied in (arbitrary) order. According to that order, exponentiation comes before multiplication. "^" is exponentiation. "-" is multiplication.

You're saying that negative numbers do not exist inherently, only as the result of a multiplicative operation performed on a numeral.

This is a somewhat true statement.

 

[Maurile Tremblay]

There are negative numbers. Negative five, for example, is a negative number.

Yes, and if you square it, you get 25, not -25.

Exactly right. If you square negative five, you get 25.But in the expression -5^2, you are not squaring negative five.

In the expression 23^2, you are not squaring three.

The operation of the minus sign comes after the operation of the exponent. The operation of converting "23" into "(2*10 + 3*1) comes before the operation of the exponent.

This is not inconsistent or illogical. "2" and "3" are numerals, as is "5". "-" is not a numeral.

Converting paired numerals into a single value comes before any operators are applied.

Then operators are applied in (arbitrary) order. According to that order, exponentiation comes before multiplication. "^" is exponentiation. "-" is multiplication.

You're saying that negative numbers do not exist inherently, only as the result of a multiplicative operation performed on a numeral.

No I'm not. Negative numbers exist inherently.It's just that they can't be represented by a single character. To represent the number negative five (which exists inherently), you have to use two characters: the numeral five following the minus sign operator.

 

[Rooster]

Seriously, this is the dumbest ####ing argument/conversation I've ever been involved in. Later morons.

I found it pretty interesting.

I find it frustrating. It's like trying to teach to someone that the color of a banana is "yellow" who thinks that's not logical, and that it should be referred to as "purple".

But if you show a banana to a bunch of say, graphics designers and artists, who you'd expect to be adept with colors and their first reaction is that the banana is purple, then something in the process is flawed and/or illogical and the "standard" of yellow is ineffective at best. I understand your point and concede that many experts recognize the standard, but I offer that since only the experts seem to recognize it that the "standard" is a useless and ineffective way of communicating with non-experts. Having a "standard" for communicating ideas that nobody besides experts recognizes is pretty useless wouldn't you say? Either spend more than 10 minutes on how to interpriet -5^2 in high school until it becomes common knowledge and get the word out so people recognize it, or start using parentheses to be clear.

 

[rolyaTy]

Just figured out that grammar is only a first order language so I couldn't come up with any exponential equivalents.But I'd still like to see my point on -1 be addressed by smoo. I don't see the issue with it.

 

[Smoo]

There are negative numbers. Negative five, for example, is a negative number.

Yes, and if you square it, you get 25, not -25.

Exactly right. If you square negative five, you get 25.But in the expression -5^2, you are not squaring negative five.

In the expression 23^2, you are not squaring three.

The operation of the minus sign comes after the operation of the exponent. The operation of converting "23" into "(2*10 + 3*1) comes before the operation of the exponent.

This is not inconsistent or illogical. "2" and "3" are numerals, as is "5". "-" is not a numeral.

Converting paired numerals into a single value comes before any operators are applied.

Then operators are applied in (arbitrary) order. According to that order, exponentiation comes before multiplication. "^" is exponentiation. "-" is multiplication.

You're saying that negative numbers do not exist inherently, only as the result of a multiplicative operation performed on a numeral.

This is a somewhat true statement.

If that's a true statement, then I no longer have a logical counter and thus it defaults to convention, which has been established.However, I'm not yet convinced that that's a true statement, although roly's vector argument is a strong place to start a counter.

I'll ponder any remaining possibilities over lunch, which is now.

 

[Smoo]

There are negative numbers. Negative five, for example, is a negative number.

Yes, and if you square it, you get 25, not -25.

Exactly right. If you square negative five, you get 25.But in the expression -5^2, you are not squaring negative five.

In the expression 23^2, you are not squaring three.

The operation of the minus sign comes after the operation of the exponent. The operation of converting "23" into "(2*10 + 3*1) comes before the operation of the exponent.

This is not inconsistent or illogical. "2" and "3" are numerals, as is "5". "-" is not a numeral.

Converting paired numerals into a single value comes before any operators are applied.

Then operators are applied in (arbitrary) order. According to that order, exponentiation comes before multiplication. "^" is exponentiation. "-" is multiplication.

You're saying that negative numbers do not exist inherently, only as the result of a multiplicative operation performed on a numeral.

No I'm not. Negative numbers exist inherently.It's just that they can't be represented by a single character. To represent the number negative five (which exists inherently), you have to use two characters: the numeral five following the minus sign operator.

You're defeating your own argument.

 

[Maurile Tremblay]

If you are arguing that only in the case of -5^2 is -5 really -(5) then the convention is stupid. But if -5 always is -(5), like I think you are arguing then the convention has nothing to do with exponents, but how to interpret the -5.

Smoo and I agree that exponents go before multiplication.Where we disagree is that I see the minus sign as an operator (whose operation is a form of multiplicatoin) while he sees it as one of the characters in a number.

 

[Boffo]

This is correct. End thread

We know it's correct by convention. We established that on page 3. Now explain why it's correct by reason. That's taken much longer and is still not resolved.

Please explain why we multiply before we subtract. I know it's by convention, but I don't understand the reasoning.

 

[rolyaTy]

There are negative numbers. Negative five, for example, is a negative number.

Yes, and if you square it, you get 25, not -25.

Exactly right. If you square negative five, you get 25.But in the expression -5^2, you are not squaring negative five.

In the expression 23^2, you are not squaring three.

The operation of the minus sign comes after the operation of the exponent. The operation of converting "23" into "(2*10 + 3*1) comes before the operation of the exponent.

This is not inconsistent or illogical. "2" and "3" are numerals, as is "5". "-" is not a numeral.

Converting paired numerals into a single value comes before any operators are applied.

Then operators are applied in (arbitrary) order. According to that order, exponentiation comes before multiplication. "^" is exponentiation. "-" is multiplication.

You're saying that negative numbers do not exist inherently, only as the result of a multiplicative operation performed on a numeral.

No I'm not. Negative numbers exist inherently.It's just that they can't be represented by a single character. To represent the number negative five (which exists inherently), you have to use two characters: the numeral five following the minus sign operator.

Yeah, the concept seems to boil down to whether or not people see -5 for what it really is, and that is 5 units in the negative direction. It's not a value, it's a magnitude and a direction. The negative sign operates on the magnitude.

 

[Smoo]

Just figured out that grammar is only a first order language so I couldn't come up with any exponential equivalents.

But I'd still like to see my point on -1 be addressed by smoo. I don't see the issue with it.

The scaler point? It's a good point. I'm working on it.

 

[Maurile Tremblay]

There are negative numbers. Negative five, for example, is a negative number.

Yes, and if you square it, you get 25, not -25.

Exactly right. If you square negative five, you get 25.But in the expression -5^2, you are not squaring negative five.

In the expression 23^2, you are not squaring three.

The operation of the minus sign comes after the operation of the exponent. The operation of converting "23" into "(2*10 + 3*1) comes before the operation of the exponent.

This is not inconsistent or illogical. "2" and "3" are numerals, as is "5". "-" is not a numeral.

Converting paired numerals into a single value comes before any operators are applied.

Then operators are applied in (arbitrary) order. According to that order, exponentiation comes before multiplication. "^" is exponentiation. "-" is multiplication.

You're saying that negative numbers do not exist inherently, only as the result of a multiplicative operation performed on a numeral.

No I'm not. Negative numbers exist inherently.It's just that they can't be represented by a single character. To represent the number negative five (which exists inherently), you have to use two characters: the numeral five following the minus sign operator.

You're defeating your own argument.

No I'm not.

 

[Smoo]

If you are arguing that only in the case of -5^2 is -5 really -(5) then the convention is stupid. But if -5 always is -(5), like I think you are arguing then the convention has nothing to do with exponents, but how to interpret the -5.

Smoo and I agree that exponents go before multiplication.Where we disagree is that I see the minus sign as an operator (whose operation is a form of multiplicatoin) while he sees it as one of the characters in a number.

 

[Maurile Tremblay]

Smoo, you know how LarryBoy uses "evolution" to mean the Big Bang theory and, even though it's a trivial thing, it screws up his thought process?You are doing the same thing by saying that negative numbers (as opposed to numerals) don't exist.

 

[Smoo]

There are negative numbers. Negative five, for example, is a negative number.

Yes, and if you square it, you get 25, not -25.

Exactly right. If you square negative five, you get 25.But in the expression -5^2, you are not squaring negative five.

In the expression 23^2, you are not squaring three.

The operation of the minus sign comes after the operation of the exponent. The operation of converting "23" into "(2*10 + 3*1) comes before the operation of the exponent.

This is not inconsistent or illogical. "2" and "3" are numerals, as is "5". "-" is not a numeral.

Converting paired numerals into a single value comes before any operators are applied.

Then operators are applied in (arbitrary) order. According to that order, exponentiation comes before multiplication. "^" is exponentiation. "-" is multiplication.

You're saying that negative numbers do not exist inherently, only as the result of a multiplicative operation performed on a numeral.

No I'm not. Negative numbers exist inherently.It's just that they can't be represented by a single character. To represent the number negative five (which exists inherently), you have to use two characters: the numeral five following the minus sign operator.

You're defeating your own argument.

No I'm not.

The number 12 can't be represented by a single character either.

 

[Paper Lions]

   

I was not trying to be an ###. Do you see a similarity Smoo?

No.

I don't agree, but I'm not going to bother explaining why I do see similarities. Carry on.Feel free to Smoo this with a response about me not doing it because I can't, or whatever Smoo-ish thing you will respond with.

 

[rolyaTy]

There are negative numbers. Negative five, for example, is a negative number.

Yes, and if you square it, you get 25, not -25.

Exactly right. If you square negative five, you get 25.But in the expression -5^2, you are not squaring negative five.

In the expression 23^2, you are not squaring three.

The operation of the minus sign comes after the operation of the exponent. The operation of converting "23" into "(2*10 + 3*1) comes before the operation of the exponent.

This is not inconsistent or illogical. "2" and "3" are numerals, as is "5". "-" is not a numeral.

Converting paired numerals into a single value comes before any operators are applied.

Then operators are applied in (arbitrary) order. According to that order, exponentiation comes before multiplication. "^" is exponentiation. "-" is multiplication.

You're saying that negative numbers do not exist inherently, only as the result of a multiplicative operation performed on a numeral.

No I'm not. Negative numbers exist inherently.It's just that they can't be represented by a single character. To represent the number negative five (which exists inherently), you have to use two characters: the numeral five following the minus sign operator.

You're defeating your own argument.

No I'm not.

The number 12 can't be represented by a single character either.

It's a magnitude in the assumed positive direction. The operator is a positive 1. There is no contradiction.

 

[Smoo]

Smoo, you know how LarryBoy uses "evolution" to mean the Big Bang theory and, even though it's a trivial thing, it screws up his thought process?

You are doing the same thing by saying that negative numbers (as opposed to numerals) don't exist.

By "don't exist", I mean "can't be represented as a self-contained unit without parentheses". Does that help?

 

[Maurile Tremblay]

There are negative numbers. Negative five, for example, is a negative number.

Yes, and if you square it, you get 25, not -25.

Exactly right. If you square negative five, you get 25.But in the expression -5^2, you are not squaring negative five.

In the expression 23^2, you are not squaring three.

The operation of the minus sign comes after the operation of the exponent. The operation of converting "23" into "(2*10 + 3*1) comes before the operation of the exponent.

This is not inconsistent or illogical. "2" and "3" are numerals, as is "5". "-" is not a numeral.

Converting paired numerals into a single value comes before any operators are applied.

Then operators are applied in (arbitrary) order. According to that order, exponentiation comes before multiplication. "^" is exponentiation. "-" is multiplication.

You're saying that negative numbers do not exist inherently, only as the result of a multiplicative operation performed on a numeral.

No I'm not. Negative numbers exist inherently.It's just that they can't be represented by a single character. To represent the number negative five (which exists inherently), you have to use two characters: the numeral five following the minus sign operator.

You're defeating your own argument.

No I'm not.

The number 12 can't be represented by a single character either.

Exactly right. And?

 

[Maurile Tremblay]

Smoo, you know how LarryBoy uses "evolution" to mean the Big Bang theory and, even though it's a trivial thing, it screws up his thought process?

You are doing the same thing by saying that negative numbers (as opposed to numerals) don't exist.

By "don't exist", I mean "can't be represented as a self-contained unit without parentheses". Does that help?

Very much.

 

[Smoo]

There are negative numbers. Negative five, for example, is a negative number.

Yes, and if you square it, you get 25, not -25.

Exactly right. If you square negative five, you get 25.But in the expression -5^2, you are not squaring negative five.

In the expression 23^2, you are not squaring three.

The operation of the minus sign comes after the operation of the exponent. The operation of converting "23" into "(2*10 + 3*1) comes before the operation of the exponent.

This is not inconsistent or illogical. "2" and "3" are numerals, as is "5". "-" is not a numeral.

Converting paired numerals into a single value comes before any operators are applied.

Then operators are applied in (arbitrary) order. According to that order, exponentiation comes before multiplication. "^" is exponentiation. "-" is multiplication.

You're saying that negative numbers do not exist inherently, only as the result of a multiplicative operation performed on a numeral.

No I'm not. Negative numbers exist inherently.It's just that they can't be represented by a single character. To represent the number negative five (which exists inherently), you have to use two characters: the numeral five following the minus sign operator.

You're defeating your own argument.

No I'm not.

The number 12 can't be represented by a single character either.

Exactly right. And?

And 12^2 <> 4.

 

[chet]

There are negative numbers. Negative five, for example, is a negative number.

Yes, and if you square it, you get 25, not -25.

Exactly right. If you square negative five, you get 25.But in the expression -5^2, you are not squaring negative five.

In the expression 23^2, you are not squaring three.

The operation of the minus sign comes after the operation of the exponent. The operation of converting "23" into "(2*10 + 3*1) comes before the operation of the exponent.

This is not inconsistent or illogical. "2" and "3" are numerals, as is "5". "-" is not a numeral.

Converting paired numerals into a single value comes before any operators are applied.

Then operators are applied in (arbitrary) order. According to that order, exponentiation comes before multiplication. "^" is exponentiation. "-" is multiplication.

You're saying that negative numbers do not exist inherently, only as the result of a multiplicative operation performed on a numeral.

No I'm not. Negative numbers exist inherently.It's just that they can't be represented by a single character. To represent the number negative five (which exists inherently), you have to use two characters: the numeral five following the minus sign operator.

You're defeating your own argument.

No I'm not.

The number 12 can't be represented by a single character either.

It can in base 12.

 

[Smoo]

Smoo, you know how LarryBoy uses "evolution" to mean the Big Bang theory and, even though it's a trivial thing, it screws up his thought process?

You are doing the same thing by saying that negative numbers (as opposed to numerals) don't exist.

By "don't exist", I mean "can't be represented as a self-contained unit without parentheses". Does that help?

Very much.

And I don't see why they shouldn't be able to. I think it would be very helpful and common sense if they could.

 

[Maurile Tremblay]

There are negative numbers. Negative five, for example, is a negative number.

Yes, and if you square it, you get 25, not -25.

Exactly right. If you square negative five, you get 25.But in the expression -5^2, you are not squaring negative five.

In the expression 23^2, you are not squaring three.

The operation of the minus sign comes after the operation of the exponent. The operation of converting "23" into "(2*10 + 3*1) comes before the operation of the exponent.

This is not inconsistent or illogical. "2" and "3" are numerals, as is "5". "-" is not a numeral.

Converting paired numerals into a single value comes before any operators are applied.

Then operators are applied in (arbitrary) order. According to that order, exponentiation comes before multiplication. "^" is exponentiation. "-" is multiplication.

You're saying that negative numbers do not exist inherently, only as the result of a multiplicative operation performed on a numeral.

No I'm not. Negative numbers exist inherently.It's just that they can't be represented by a single character. To represent the number negative five (which exists inherently), you have to use two characters: the numeral five following the minus sign operator.

You're defeating your own argument.

No I'm not.

The number 12 can't be represented by a single character either.

Exactly right. And?

And 12^2 <> 4.

Exactly. As I explained above, converting "12" into "(1*10 + 2*1)" comes before exponentiation (or any other operator). And?

 

[Smoo]

There are negative numbers. Negative five, for example, is a negative number.

Yes, and if you square it, you get 25, not -25.

Exactly right. If you square negative five, you get 25.But in the expression -5^2, you are not squaring negative five.

In the expression 23^2, you are not squaring three.

The operation of the minus sign comes after the operation of the exponent. The operation of converting "23" into "(2*10 + 3*1) comes before the operation of the exponent.

This is not inconsistent or illogical. "2" and "3" are numerals, as is "5". "-" is not a numeral.

Converting paired numerals into a single value comes before any operators are applied.

Then operators are applied in (arbitrary) order. According to that order, exponentiation comes before multiplication. "^" is exponentiation. "-" is multiplication.

You're saying that negative numbers do not exist inherently, only as the result of a multiplicative operation performed on a numeral.

No I'm not. Negative numbers exist inherently.It's just that they can't be represented by a single character. To represent the number negative five (which exists inherently), you have to use two characters: the numeral five following the minus sign operator.

You're defeating your own argument.

No I'm not.

The number 12 can't be represented by a single character either.

It can in base 12.

Actually, no it can't. 12 in base 12 is 10. You need base 13 or higher.

 

[bagger.]

so under new math 12 is not 12, but rather 1 x 12 (and the 1 x is assumed).likewise -12 is not -12, but rather -1 x 12.new math sucks.

 

[Smoo]

Exactly. As I explained above, converting "12" into "(1*10 + 2*1)" comes before exponentiation (or any other operator). And?

Interesting.

 

[dgreen]

so under new math 12 is not 12, but rather 1 x 12 (and the 1 x is assumed).

likewise -12 is not -12, but rather -1 x 12.

new math sucks.

When I see -5^2, I assume -5 is made up of (-2)(2.5). Therefore, -5^2 = -12.5.

 

[FatMax]

Smoo, you know how LarryBoy uses "evolution" to mean the Big Bang theory and, even though it's a trivial thing, it screws up his thought process?

You are doing the same thing by saying that negative numbers (as opposed to numerals) don't exist.

Fifteen yard penalty and a swift kick to the nuts for a comparison to larry.

 

[Maurile Tremblay]

The number 12 can't be represented by a single character either.

It can in base 12.

This is actually an awesome point. We've been discussing syntax for base ten. In base ten, there are only ten numerals, 0 through 9.

One of the numerals has a neutral value, the other nine have a positive value.

No numerals have a negative value.

 

[jonessed]

My HP 48G evaluates -5^2 (no parantheses) as 25.  Apparently HPs mathematicians got it wrong too?  I don't know of a more commonly used calculator amongst engineering students.

MS Excel does the same thing, but their programmers specifically acknowledged that they were flouting convention.

Why would HPs mathematicians flout convention? And where do they state that they are doing this?

 

[Bottomfeeder Sports]

If you are arguing that only in the case of -5^2 is -5 really -(5)  then the convention is stupid.  But if -5 always is -(5), like I think you are arguing then the convention has nothing to do with exponents, but how to interpret the -5.

Smoo and I agree that exponents go before multiplication.Where we disagree is that I see the minus sign as an operator (whose operation is a form of multiplicatoin) while he sees it as one of the characters in a number.

An how is that not?Maurile: -5 = -(5)

Smoo: -5 = (-5)

Or if you prefer

Smoo sees -5^2 as x^2 where x = -5

Maurile sees -5^2 as -x^2 where x = 5

 

[Buckychudd]

There are negative numbers. Negative five, for example, is a negative number.

Yes, and if you square it, you get 25, not -25.

Exactly right. If you square negative five, you get 25.But in the expression -5^2, you are not squaring negative five.

In the expression 23^2, you are not squaring three.

The operation of the minus sign comes after the operation of the exponent. The operation of converting "23" into "(2*10 + 3*1) comes before the operation of the exponent.

This is not inconsistent or illogical. "2" and "3" are numerals, as is "5". "-" is not a numeral.

Converting paired numerals into a single value comes before any operators are applied.

Then operators are applied in (arbitrary) order. According to that order, exponentiation comes before multiplication. "^" is exponentiation. "-" is multiplication.

You're saying that negative numbers do not exist inherently, only as the result of a multiplicative operation performed on a numeral.

This is a somewhat true statement.

If that's a true statement, then I no longer have a logical counter and thus it defaults to convention, which has been established.However, I'm not yet convinced that that's a true statement, although roly's vector argument is a strong place to start a counter.

I'll ponder any remaining possibilities over lunch, which is now.

Ok, you already saw this explained in the "Universe" thread but here goes.Please hand me -5 apples, I would like to feel and taste them. Please show me the object with a negative mass, please show me two objects that have negative distance between them, please show me an object that has negative velocity.

The negative signifies something is to be taken away, but does not exist in reality. I may owe you 5 apples, meaning I have -5 apples.....but I don't actually have in my possession -5 apples.

 

[bagger.]

honestly, i always took -5^2 = -5 x -5 = 25is that old math?why did it change?

 

[dgreen]

honestly, i always took -5^2 = -5 x -5 = 25

is that old math?

why did it change?

And when did it change? This may have been covered on like page 10, but I'm late here and I'm not going back.

 

[660]

Using smoo's rules then I expect an augument from him soon about spelling the word fish like this...ghoti [enouGH] + [wOmen] + [moTIon]Can we talk about real math please, and not these symantics.

 

[Maurile Tremblay]

My HP 48G evaluates -5^2 (no parantheses) as 25. Apparently HPs mathematicians got it wrong too? I don't know of a more commonly used calculator amongst engineering students.

MS Excel does the same thing, but their programmers specifically acknowledged that they were flouting convention.

Why would HPs mathematicians flout convention? And where do they state that they are doing this?

Somewhere around page 12, I believe.

 

[Clayton Gray]

I would like to point out that this is a middle school concept.  People that were math nerds in middle school often bypassed the regular math classes and went straight to Algebra.  It is completely possible that they missed being taught this and are relying upon their incorrect intuition.

So - if you get -25 you were either not very good at math so you went to the basics classes in 8th grade on, or you are trained as a math teachers. (What is that cliche about those who teach?) But you get feel all superior about technically being correct.

All I said was that it's possible. No need to be defensive.

 

[Paper Lions]

honestly, i always took -5^2 = -5 x -5 = 25

is that old math?

why did it change?

And when did it change? This may have been covered on like page 10, but I'm late here and I'm not going back.

According to the math , it never changed. We were not properly taught in school the convention for -5^2 in an algebra equation.

 

[Ignoramus]

honestly, i always took -5^2 = -5 x -5 = 25

is that old math?

why did it change?

And when did it change? This may have been covered on like page 10, but I'm late here and I'm not going back.

Another seventeen pages.

 

[FatMax]

Please hand me -5 apples, I would like to feel and taste them. Please show me the object with a negative mass, please show me two objects that have negative distance between them, please show me an object that has negative velocity.

Negative velocity is easily explained by vectors. I agree with Smoo. This is a better place to start.

 

[bagger.]

honestly, i always took -5^2 = -5 x -5 = 25

is that old math?

why did it change?

And when did it change? This may have been covered on like page 10, but I'm late here and I'm not going back.

According to the math , it never changed. We were not properly taught in school the convention for -5^2 in an algebra equation.

so is this akin to people being taught the world was flat and their children were taught that it was round?ARE YOU SAYING I WAS TAUGHT THE WRONG WAY??

there's a lawsuit in here somewhere.

 

[dgreen]

honestly, i always took -5^2 = -5 x -5 = 25

is that old math?

why did it change?

And when did it change? This may have been covered on like page 10, but I'm late here and I'm not going back.

According to the math , it never changed. We were not properly taught in school the convention for -5^2 in an algebra equation.

Figures. Is this where we hijack the thread to discuss public education? Then again, I may have been asleep that day.

 

[Maurile Tremblay]

If you are arguing that only in the case of -5^2 is -5 really -(5) then the convention is stupid. But if -5 always is -(5), like I think you are arguing then the convention has nothing to do with exponents, but how to interpret the -5.

Smoo and I agree that exponents go before multiplication.Where we disagree is that I see the minus sign as an operator (whose operation is a form of multiplicatoin) while he sees it as one of the characters in a number.

An how is that not?Maurile: -5 = -(5)

Smoo: -5 = (-5)

Smoo and I both agree that -5 = (-5) = -(5). There's only one operator there, so it doesn't matter in what order you apply it relative to other operators, or even whether you treat it as an operator at all.

Or if you prefer

Smoo sees -5^2 as x^2 where x = -5

Maurile sees -5^2 as -x^2 where x = 5

This is correct.

 

[Buckychudd]

Please hand me -5 apples, I would like to feel and taste them.  Please show me the object with a negative mass, please show me two objects that have negative distance between them, please show me an object that has negative velocity.

Negative velocity is easily explained by vectors. I agree with Smoo. This is a better place to start.

Negative velocity is just a positive velocity that is going the other way, there is no such thing as an actual negative velocity.

 

[John 14:6]

This is correct.  End thread 

We know it's correct by convention. We established that on page 3. Now explain why it's correct by reason. That's taken much longer and is still not resolved.

Please explain why we multiply before we subtract. I know it's by convention, but I don't understand the reasoning.

Has anyone asked about the square root of -1 yet?

 

[jonessed]

There are negative numbers. Negative five, for example, is a negative number.

Yes, and if you square it, you get 25, not -25.

Exactly right. If you square negative five, you get 25.But in the expression -5^2, you are not squaring negative five.

In the expression 23^2, you are not squaring three.

The operation of the minus sign comes after the operation of the exponent. The operation of converting "23" into "(2*10 + 3*1) comes before the operation of the exponent.

This is not inconsistent or illogical. "2" and "3" are numerals, as is "5". "-" is not a numeral.

Converting paired numerals into a single value comes before any operators are applied.

Then operators are applied in (arbitrary) order. According to that order, exponentiation comes before multiplication. "^" is exponentiation. "-" is multiplication.

You're saying that negative numbers do not exist inherently, only as the result of a multiplicative operation performed on a numeral.

This is a somewhat true statement.

If that's a true statement, then I no longer have a logical counter and thus it defaults to convention, which has been established.However, I'm not yet convinced that that's a true statement, although roly's vector argument is a strong place to start a counter.

I'll ponder any remaining possibilities over lunch, which is now.

Ok, you already saw this explained in the "Universe" thread but here goes.Please hand me -5 apples, I would like to feel and taste them. Please show me the object with a negative mass, please show me two objects that have negative distance between them, please show me an object that has negative velocity.

The negative signifies something is to be taken away, but does not exist in reality. I may owe you 5 apples, meaning I have -5 apples.....but I don't actually have in my possession -5 apples.

I can show you an object that has negative acceleration.

 

[Boffo]

There are negative numbers. Negative five, for example, is a negative number.

Yes, and if you square it, you get 25, not -25.

Exactly right. If you square negative five, you get 25.But in the expression -5^2, you are not squaring negative five.

In the expression 23^2, you are not squaring three.

The operation of the minus sign comes after the operation of the exponent. The operation of converting "23" into "(2*10 + 3*1) comes before the operation of the exponent.

This is not inconsistent or illogical. "2" and "3" are numerals, as is "5". "-" is not a numeral.

Converting paired numerals into a single value comes before any operators are applied.

Then operators are applied in (arbitrary) order. According to that order, exponentiation comes before multiplication. "^" is exponentiation. "-" is multiplication.

You're saying that negative numbers do not exist inherently, only as the result of a multiplicative operation performed on a numeral.

This is a somewhat true statement.

If that's a true statement, then I no longer have a logical counter and thus it defaults to convention, which has been established.However, I'm not yet convinced that that's a true statement, although roly's vector argument is a strong place to start a counter.

I'll ponder any remaining possibilities over lunch, which is now.

Ok, you already saw this explained in the "Universe" thread but here goes.Please hand me -5 apples, I would like to feel and taste them. Please show me the object with a negative mass, please show me two objects that have negative distance between them, please show me an object that has negative velocity.

The negative signifies something is to be taken away, but does not exist in reality. I may owe you 5 apples, meaning I have -5 apples.....but I don't actually have in my possession -5 apples.

I agree with everything you said except the "negative velocity". I thought that velocity is a vector, and therefore it can be negative? It just means "to the left" (or opposite to w/e the positive direction of motion would be)?

 

[Buckychudd]

This is correct.  End thread 

We know it's correct by convention. We established that on page 3. Now explain why it's correct by reason. That's taken much longer and is still not resolved.

Please explain why we multiply before we subtract. I know it's by convention, but I don't understand the reasoning.

Has anyone asked about the square root of -1 yet?

 

[Maurile Tremblay]

honestly, i always took -5^2 = -5 x -5 = 25

is that old math?

why did it change?

And when did it change? This may have been covered on like page 10, but I'm late here and I'm not going back.

According to the math , it never changed. We were not properly taught in school the convention for -5^2 in an algebra equation.

so is this akin to people being taught the world was flat and their children were taught that it was round?

No, it's like some people are taught to drive on the left-hand side of the street while others are taught to drive on the right-hand side of the street.There's no inherently correct answer: it just depends on soceity's conventions. There may be different conventions in different times or places.

 

[dgreen]

Please hand me -5 apples, I would like to feel and taste them. Please show me the object with a negative mass, please show me two objects that have negative distance between them, please show me an object that has negative velocity.

Negative velocity is easily explained by vectors. I agree with Smoo. This is a better place to start.

Negative velocity is just a positive velocity that is going the other way, there is no such thing as an actual negative velocity.

So when Portis runs for negative yardage, I should argue that it is actually positive yardage just going the other way and have it added back into his totals?