Daughter's math homework (1 Viewer)

[FatMax]

When he rewrites -5 as (-1)(5) he's not "factoring it out." He's rewriting it -- correctly, by convention.

Well I must not know what factoring is. Because in my mind, it looks exactly like that.

 

[FatMax]

When he rewrites -5 as (-1)(5) he's not "factoring it out." He's rewriting it -- correctly, by convention.

Well I must not know what factoring is. Because in my mind, it looks exactly like that.

But in Shicks defense, he never used the word 'factor' to describe what he was doing.

 

[Maurile Tremblay]

To believe there is a multiplication is to believe there is no such thing as a negative number.

This is simply wrong. There are such things as negative numbers. There are in fact an infinite number of them.If you want negative five to be treated as its own value, write it as (-5). Don't write it as -1 * 5.

Uhh, nut of the examples below, which looks more correct to you?

-4 + 5 = 1

(-4) + 5 = 1

Parenthesis are unnecessary to convey that a number is negative.

Those are both the same since subtraction and addition are equal in priority. The parentheses aren't needed in that example since the expressions get resolved the same way in either case.But if the first term had an exponent, that would no longer be true.

 

[jonessed]

An interesting side note. I'm an engineer (about 7 years removed from college) and answered 25 (to the solution of -5^2 in the first problem), but I don't really practive traditional engineering so I figured I might be a bit out of the loop. I tossed a friend of mine who currently works for a civil engineering firm this problem and he also answered 25. We then became curious as to how the other practicing engineers (in this case civil and structural) would answer given the same notation and he sent out an email to his peers. He had 18 replies and all of them were 25 as well. (Update: it's 17 and 3 now; someone changed their first answer and two new ones came in )That's not to say that this is the proper arithmetic nor is this obviously a satisfactory sampling of industry (given the confusion in the thread a large sampling would undoubtedly give answers going both ways), BUT I think it is important to note that if it doesn't translate to where people will likely be using it then it doesn't mean much. At the very least there is some serious confusion and it doesn't stop with just Mom and Dad remembering High School math .Edit: The answer of -25 seems accurate to me now given the logic. I don't think it's most people's off the cuff answer though unless they are teaching it. Just a guess.

 

[[icon]]

I think Shick! cleared it all up.

What does shick! know about maff?

 

[rolyaTy]

Here's the most concise logical explanation I can muster:The answer is that it doesn't matter that -5 is an integer or not, the negative sign is a direction that modifies the value of 5. Five exists, negative five does not. Negative five is only Five in a specific direction. The negative sign is an operator on the value of five. As it's an operator, it's subject to the order of operations, and comes UNDER the priority of exponents, unless parentheses say otherwise.

 

[Smoo]

To believe there is a multiplication is to believe there is no such thing as a negative number.

This is simply wrong. There are such things as negative numbers. There are in fact an infinite number of them.If you want negative five to be treated as its own value, write it as (-5). Don't write it as -1 * 5.

Nobody wrote it as -1 * 5. This is an assumption that has been made, based on the assertion that -5 is not a number but an operation. -5 is a number.

By convention, -5 is the same as -1 * 5.You understand this already.

It doesn't mean that negative numbers don't exist, or can't be expressed as such. Just write "(-5)".

Remember the post where I was role-playing? Do you see the fallacy of your argument now? I'm trying to establish the reaosning for the convention, and you're invoking the actual convention to do it. You're making the same mistake here that you often call out biblical apologists for.

No, I'm refuting your assertion that the current convention implies that negative numbers don't exist.

I will clarify then. Current convention implies that the only negative number that exists is -1 and all other negative numbers are to be considered multiplicative operations with the designated negative.

 

[Smoo]

Here's the most concise logical explanation I can muster:

The answer is that it doesn't matter that -5 is an integer or not, the negative sign is a direction that modifies the value of 5. Five exists, negative five does not. Negative five is only Five in a specific direction. The negative sign is an operator on the value of five. As it's an operator, it's subject to the order of operations, and comes UNDER the priority of exponents, unless parentheses say otherwise.

roly has provided the only argument so far which has any chance of swaying me.

 

[Kleck]

Hey Smoo,I understand you're attempting to explain this in a way that makes sense for you, and I don't disagree that work falls on our lap to help you understand. If I understand the block for you it revolves around the concept of "-5" being its own entity. Its own number.If so, I can try to show you why its not in two different ways.First, can you represent "-5" in terms of some real thing? Some group of objects? Where do you encounter "-5"? Whatever example you use, you're really showing us the opposite of some +5 value.Second, there's an established hierarchy of numbers. They are...NATURAL --> WHOLE --> INTEGER --> RATIONALNaturals = 1,2,3 ...Whole = 0,1,2,3 ...Integers = ...-3,-2,-1,0,1,2,3 ...Rationals = Any number that can be represented as a ratio of two integers.The natural numbers are the basis of all real numbers. Can you see that the integers are based on the naturals? Just as rational numbers are formed by a ratio of integers? Any negative integer is really "the opposite of" some positive natural number.Does this help?

 

[rolyaTy]

To believe there is a multiplication is to believe there is no such thing as a negative number.

This is simply wrong. There are such things as negative numbers. There are in fact an infinite number of them.If you want negative five to be treated as its own value, write it as (-5). Don't write it as -1 * 5.

Nobody wrote it as -1 * 5. This is an assumption that has been made, based on the assertion that -5 is not a number but an operation. -5 is a number.

By convention, -5 is the same as -1 * 5.You understand this already.

It doesn't mean that negative numbers don't exist, or can't be expressed as such. Just write "(-5)".

Remember the post where I was role-playing? Do you see the fallacy of your argument now? I'm trying to establish the reaosning for the convention, and you're invoking the actual convention to do it. You're making the same mistake here that you often call out biblical apologists for.

No, I'm refuting your assertion that the current convention implies that negative numbers don't exist.

I will clarify then. Current convention implies that the only negative number that exists is -1 and all other negative numbers are to be considered multiplicative operations with the designated negative.

Negative numbers don't exist. Negativity is a theoretical concept and is relevant only when dealing with a frame of reference. -3 is 3 units in the left direction of 0 on a number line. Negativity and positivity only imply direction and have no bearing on the numerical value of any number. That is why it's considered an operator, and it's subserviant to exponents.-1 doesn't exist either in real life. It's a concept that has two parts, a value and a direction.

 

[Smoo]

Hey Smoo,

I understand you're attempting to explain this in a way that makes sense for you, and I don't disagree that work falls on our lap to help you understand. If I understand the block for you it revolves around the concept of "-5" being its own entity. Its own number.

If so, I can try to show you why its not in two different ways.

First, can you represent "-5" in terms of some real thing? Some group of objects? Where do you encounter "-5"? Whatever example you use, you're really showing us the opposite of some +5 value.

Second, there's an established hierarchy of numbers. They are...

NATURAL --> WHOLE --> INTEGER --> RATIONAL

Naturals = 1,2,3 ...

Whole = 0,1,2,3 ...

Integers = ...-3,-2,-1,0,1,2,3 ...

Rationals = Any number that can be represented as a ratio of two integers.

The natural numbers are the basis of all real numbers. Can you see that the integers are based on the naturals? Just as rational numbers are formed by a ratio of integers? Any negative integer is really "the opposite of" some positive natural number.

Does this help?

Only marginally. Roly's vector explanation was better.

 

[Kleck]

Current convention implies that the only negative number that exists is -1 and all other negative numbers are to be considered multiplicative operations with the designated negative.

Not completely true. -1 is "the opposite of positive one".

 

[munga30]

I am *El Cyclone,* from... Bolivia. One-man gang. This classroom is *my* domain. Don't give me no gas, or I'll jump on your face and tattoo your chromosomes... If the only thing you know how to do is add and subtract, you will only be prepared to do one thing: Pump gas.

 

[tommyboy]

answer this then:-4^3 x 3^4 x -2^2 =

 

[munga30]

Tough guys don't do math. Tough guys fry chicken for a living.

 

[munga30]

Hey, I'm the first one here. What's calcoolus?

 

[Smoo]

-1 doesn't exist either in real life. It's a concept that has two parts, a value and a direction.

And this is the only thing keeping me in opposition to you guys. At some point your argument achieves a state in which -1 has to exist as a self-contained entity or else devolve into infinite regression. And if -1 is a self-contained entity, why not -5 as well?

 

[bryhamm]

answer this then:

-4^3 x 3^4 x -2^2 =

20736

 

[Maurile Tremblay]

I will clarify then. Current convention implies that the only negative number that exists is -1 and all other negative numbers are to be considered multiplicative operations with the designated negative.

I think you're confusing numbers with numerals. An infinitie number of negative numbers exist. No negative numerals exist.

 

[munga30]

-2 + 2... fill de hole...

 

[Smoo]

I will clarify then. Current convention implies that the only negative number that exists is -1 and all other negative numbers are to be considered multiplicative operations with the designated negative.

I think you're confusing numbers with numerals. An infinitie number of negative numbers exist. No negative numerals exist.

Except -1.

 

[FatMax]

Here's the most concise logical explanation I can muster:

The answer is that it doesn't matter that -5 is an integer or not, the negative sign is a direction that modifies the value of 5.  Five exists, negative five does not.  Negative five is only Five in a specific direction.  The negative sign is an operator on the value of five.  As it's an operator, it's subject to the order of operations, and comes UNDER the priority of exponents, unless parentheses say otherwise.

roly has provided the only argument so far which has any chance of swaying me.

DON'T DO IT!!

 

[Smoo]

Here's the most concise logical explanation I can muster:

The answer is that it doesn't matter that -5 is an integer or not, the negative sign is a direction that modifies the value of 5. Five exists, negative five does not. Negative five is only Five in a specific direction. The negative sign is an operator on the value of five. As it's an operator, it's subject to the order of operations, and comes UNDER the priority of exponents, unless parentheses say otherwise.

roly has provided the only argument so far which has any chance of swaying me.

DON'T DO IT!!

He won't be able to resolve the -1 issue.

 

[MrPack]

answer this then:

-4^3 x 3^4 x -2^2 =

20,736

 

[Kleck]

I will clarify then.  Current convention implies that the only negative number that exists is -1 and all other negative numbers are to be considered multiplicative operations with the designated negative.

I think you're confusing numbers with numerals. An infinitie number of negative numbers exist. No negative numerals exist.

Except -1.

No. Don't get hung up here. That's the opposite of the natural number one.

 

[FatMax]

An interesting side note.

I'm an engineer (about 7 years removed from college) and answered 25 (to the solution of -5^2 in the first problem), but I don't really practive traditional engineering so I figured I might be a bit out of the loop. I tossed a friend of mine who currently works for a civil engineering firm this problem and he also answered 25. We then became curious as to how the other practicing engineers (in this case civil and structural) would answer given the same notation and he sent out an email to his peers. He had 18 replies and all of them were 25 as well. (Update: it's 17 and 3 now; someone changed their first answer and two new ones came in )

That's not to say that this is the proper arithmetic nor is this obviously a satisfactory sampling of industry (given the confusion in the thread a large sampling would undoubtedly give answers going both ways), BUT I think it is important to note that if it doesn't translate to where people will likely be using it then it doesn't mean much. At the very least there is some serious confusion and it doesn't stop with just Mom and Dad remembering High School math .

Edit: The answer of -25 seems accurate to me now given the logic. I don't think it's most people's off the cuff answer though unless they are teaching it. Just a guess.

This post needs more love. Add one more engineer to your list that got it wrong the first time.

 

[(HULK)]

First, can you represent "-5" in terms of some real thing? Some group of objects? Where do you encounter "-5"? Whatever example you use, you're really showing us the opposite of some +5 value.

Its a real conceptual number... just as 0 is as well.You can't show me zero apples. You can claim to show me zero apples, but I could claim that you're showing me zero oranges instead.

 

[Smoo]

I will clarify then. Current convention implies that the only negative number that exists is -1 and all other negative numbers are to be considered multiplicative operations with the designated negative.

I think you're confusing numbers with numerals. An infinitie number of negative numbers exist. No negative numerals exist.

Except -1.

No. Don't get hung up here. That's the opposite of the natural number one.

You use it as a self-contained number. You don't factor it out to (-1)(1) as you do with -5. Why is that?

 

[bryhamm]

answer this then:

-4^3 x 3^4 x -2^2 =

20,736

This was a bad example. Regardless of which side of this debate you are on or not, both sides will get the same answer. It would have been better to only have one of the "-" signs in the example.

 

[rolyaTy]

Here's the most concise logical explanation I can muster:

The answer is that it doesn't matter that -5 is an integer or not, the negative sign is a direction that modifies the value of 5. Five exists, negative five does not. Negative five is only Five in a specific direction. The negative sign is an operator on the value of five. As it's an operator, it's subject to the order of operations, and comes UNDER the priority of exponents, unless parentheses say otherwise.

roly has provided the only argument so far which has any chance of swaying me.

DON'T DO IT!!

He won't be able to resolve the -1 issue.

I don't see the issue with -1. It's just 1 step in the negative direction. It's a unit vector, used to scale other magnitudes in the same direction.

 

[Sam Quentin]

I think RoyAlty may have swayed him.If all numbers quantities and + and - signs are directions and conventions says that parens>exponent ops>*/>+-then it should make sense to him

 

[rick6668]

answer this then:

-4^3 x 3^4 x -2^2 =

-4^3 x 3^4 x -2^2 =-64 * 81 * 4 = -20736

Because you listed * -2^2, having 2 operators in a row shows that the -2 is the same as (-2). The - is part of the value. When you don't specify as is -4^3, the negative is an operator.

 

[bryhamm]

First, can you represent "-5" in terms of some real thing? Some group of objects? Where do you encounter "-5"? Whatever example you use, you're really showing us the opposite of some +5 value.

Its a real conceptual number... just as 0 is as well.You can't show me zero apples. You can claim to show me zero apples, but I could claim that you're showing me zero oranges instead.

Which is why Shick! pointed out:

Naturals = 1,2,3 ...

Whole = 0,1,2,3 ...

Integers = ...-3,-2,-1,0,1,2,3 ...

Rationals = Any number that can be represented as a ratio of two integers.

0 is not a natural number.

 

[Smoo]

Here's the most concise logical explanation I can muster:

The answer is that it doesn't matter that -5 is an integer or not, the negative sign is a direction that modifies the value of 5. Five exists, negative five does not. Negative five is only Five in a specific direction. The negative sign is an operator on the value of five. As it's an operator, it's subject to the order of operations, and comes UNDER the priority of exponents, unless parentheses say otherwise.

roly has provided the only argument so far which has any chance of swaying me.

DON'T DO IT!!

He won't be able to resolve the -1 issue.

I don't see the issue with -1. It's just 1 step in the negative direction. It's a unit vector, used to scale other magnitudes in the same direction.

It's being used as an inherently negative number. All other negative numbers seem to require factoring. This is inconsistent. Math isn't inconsistent.

 

[Sid]

Hey, I'm the first one here. What's calcoolus?

I love that scene.."I killed him, he's decomposing in my locker..."

 

[(HULK)]

First, can you represent "-5" in terms of some real thing? Some group of objects? Where do you encounter "-5"? Whatever example you use, you're really showing us the opposite of some +5 value.

Its a real conceptual number... just as 0 is as well.You can't show me zero apples. You can claim to show me zero apples, but I could claim that you're showing me zero oranges instead.

Which is why Shick! pointed out:

Naturals = 1,2,3 ...

Whole = 0,1,2,3 ...

Integers = ...-3,-2,-1,0,1,2,3 ...

Rationals = Any number that can be represented as a ratio of two integers.

0 is not a natural number.

That doesn't stop it from existing.

 

[Smoo]

I think RoyAlty may have swayed him.

If all numbers quantities and + and - signs are directions and conventions says that parens>exponent ops>*/>+-

then it should make sense to him

The vector argument is sensible in theory, but in practice -1 seems to be an exception. Until this has been resolved, there is no swaying.

 

[tommyboy]

answer this then:

-4^3 x 3^4 x -2^2 =

20736

now answer it this way-4^3 x 3^4 x -2^2 x -1^2

 

[Smoo]

answer this then:

-4^3 x 3^4 x -2^2 =

20736

now answer it this way-4^3 x 3^4 x -2^2 x -1^2

Multiplying it by 1 doesn't change the answer.

 

[Mjolnirs]

answer this then:

-4^3 x 3^4 x -2^2 =

20736

-4^3 x 3^4 x -2^2-64 x 81 x 4

-20736

 

[Maurile Tremblay]

-1 is not a numeral. 1 is a numeral expressing the value of one. -1 is an expression containing two characters (an operator and a numeral) that means the opposite of the value of one.

 

[bryhamm]

answer this then:

-4^3 x 3^4 x -2^2 =

20736

now answer it this way-4^3 x 3^4 x -2^2 x -1^2

-20736

answer this then:

-4^3 x 3^4 x -2^2 =

20736

now answer it this way-4^3 x 3^4 x -2^2 x -1^2

Multiplying it by 1 doesn't change the answer.

It is not multiplying it by 1, it is multiplying it by -1 which was arrived at by squaring 1 and then taking the opposit of that answer.

 

[Kleck]

You use it as a self-contained number. You don't factor it out to (-1)(1) as you do with -5. Why is that?

Sure I do, but I don't write it that way, and I don't think about it in those terms. I prefer to use the words "opposite of". I'm sure you understand that we don't always use the best conventions when writing out what we mean due to expediency and convenience. Its been forever since I had a number theory class. I may not be the best person available to have this discussion with. Dr. Drinen could probably clear this up much quicker than I can for you. Sending him a quick PM would probably be a solid idea.

 

[Smoo]

-1 is not a numeral. 1 is a numeral expressing the value of one. -1 is an expression containing two characters (an operator and a numeral) that means the opposite of the value of one.

So it actually means (-1)(1). That's exactly what you're saying.Infinite regression.

 

[rick6668]

answer this then:

-4^3 x 3^4 x -2^2 =

20736

now answer it this way-4^3 x 3^4 x -2^2 x -1^2

Multiplying it by 1 doesn't change the answer.

Putting two operators right next to each other forces you to include the minus sign as part of the number. 1 x -4^3 x 3^4 x -2^2 x -1^2 != -4^3 x 3^4 x -2^2 x -1^2

 

[Maurile Tremblay]

-1 is not a numeral. 1 is a numeral expressing the value of one. -1 is an expression containing two characters (an operator and a numeral) that means the opposite of the value of one.

So it actually means (-1)(1). That's exactly what you're saying.Infinite regression.

It means the opposite of one, which can also (but doesn't have to be) written as (-1)(1).Similarly, 1 can be written as (1)(1) -- but that doesn't turn it into an infinite regression, either.

 

[Buckychudd]

Ok, I don't know about all this no negative number crap, but can someone please answer me this!What =(-1)^(1/2)

 

[Kleck]

This is inconsistent. Math isn't inconsistent.

I agree. Math is consistent, but human beings are often inconsistent in the notation we use to convey a meaning.

 

[Maurile Tremblay]

Ok, I don't know about all this no negative number crap, but can someone please answer me this!

What =(-1)^(1/2)

i

 

[Kleck]

Ok, I don't know about all this no negative number crap, but can someone please answer me this!

What =(-1)^(1/2)

i