Daughter's math homework (1 Viewer)

[Thorn]

It is clearly not universally accepted, see this thread.

To say there is "clearly" not a universally accepted convention is just wrong. This is akin to a person standing outside on a sunny day pointing at the sky claiming that is actually raining constitutes enough of an opposition to argue against a universal convention of what precipitation means.If you put 1000 random high school and college mathematics professors in a room you're going to find a few of them that will argue that there is some ambiguity while the other 990+ just sort of roll their eyes into their heads wondering why anyone would bother wasting time with the argument.

I didn't realize that question was directed at me. Do mathematicians have a national association?

There are many national and worldwide associations of mathematicians. Currently I belong to the NCTM and I routinely participate in the forums at Drexel University. One of the popular forums there is Ask Dr. Math. This same discussion has taken place many times. Yes, there are a few holdouts that argue against the convention just like you will find in any other arena, but the reality is that the overwhelming majority of professionals in the mathematics field agree on the convention.

Your definition of universal is really weird. Not everyone accepts the convention if there are holdouts even among mathematicians.

 

[bostonfred]

-5 is not a shorthand way of saying -15.

I'm not sure whom you're arguing with here. Has anybody contended that -5 is a shorthand way of saying -15? If you think the answer is yes, I suspect you are misunderstanding people's arguments.

You can't trust Fred. He turned the Don/Dawn debate into a mess.

They're pronounced the same.The thing is, I think bostonfred already stated a few pages ago (unless I'm remembering wrong) that -5^2 = -25 according to what the convention actually is. He just thinks that -5^2 = 25 under what the convention should be, if the convention were to make more sense. That's similar to the view Smoo undertook.

That's fine. People can reasonably disagree about what the convention should be. There may be decent arguments on both sides.

But the question of what the standard convention actually is appears to be definitively settled. So I don't know why people (including bostonfred, unless I'm misreading his most recent posts) are continuing to discuss that question.

I agree that many calculator manufacturers have programmed their computers this way, and that many teachers and professors teach that this is the correct way to handle it. I feel strongly that the convention is wrong. I disagree with some of the statements that have been made defending the convention. And I disagree with some of the statement made by people who disagree with the convention, too. I particularly disagree with the whole "written as" thing, because notational equivalence is not the same as mathematical equivalence, and that's the issue that causes the whole misunderstanding in the first place.

 

[Maurile Tremblay]

-5 is not a shorthand way of saying -15.

I'm not sure whom you're arguing with here. Has anybody contended that -5 is a shorthand way of saying -15? If you think the answer is yes, I suspect you are misunderstanding people's arguments.

My contention is as follows:If x = 5, -x^2 = -25.

However, -5^2 =25, NOT -25.

In posts #1381 and #1383, you said that you don't question the existence of the convention [that exponents precede the unary minus in the order of operations] even though the convention doesn't lend itself to clear mathematical convention.I took that as an acknowledgment that the standard convention is to resolve the exponent before the unary minus, such that -5^2 = -25. Are you changing your mind? Or did I misunderstand your previous posts?

Yet you specifically have argued that -5 is the notational equivalent of saying -1*5. That is not true. It's the mathematical equivalent, not the notational equivalent. As such, you may replace -5 with (-1*5) or even ((-1)*(5)) if you prefer. But you can't replace it without using parentheses around it, anymore than you can replace it with 17-22 without using parentheses.

I said that the value most simply expressed as "-5" can be expressed in a variety of other ways as well, including "-1*5".I didn't say anything about replacing different expressions with each other, as if we're working with character strings.

 

[bostonfred]

You can't trust Fred. He turned the Don/Dawn debate into a mess.

They're pronounced the same.

Exactly

 

[jon_mx]

So some here are honestly telling me that 5^2 - 5^2= 50?

No, but what is 5^2+-5^2? I would say that is 50, because to me that says plus negative 5 squared, not minus 5 squared.

 

[Ilov80s]

So some here are honestly telling me that 5^2 - 5^2= 50?

No, but what is 5^2+-5^2? I would say that is 50, because to me that says plus negative 5 squared, not minus 5 squared.

That would be simplified to 5^2 - 5^2 and thus give the same result: 0

 

[Ilov80s]

-5 is not a shorthand way of saying -15.

I'm not sure whom you're arguing with here. Has anybody contended that -5 is a shorthand way of saying -15? If you think the answer is yes, I suspect you are misunderstanding people's arguments.

You can't trust Fred. He turned the Don/Dawn debate into a mess.

They're pronounced the same.The thing is, I think bostonfred already stated a few pages ago (unless I'm remembering wrong) that -5^2 = -25 according to what the convention actually is. He just thinks that -5^2 = 25 under what the convention should be, if the convention were to make more sense. That's similar to the view Smoo undertook.

That's fine. People can reasonably disagree about what the convention should be. There may be decent arguments on both sides.

But the question of what the standard convention actually is appears to be definitively settled. So I don't know why people (including bostonfred, unless I'm misreading his most recent posts) are continuing to discuss that question.

I agree that many calculator manufacturers have programmed their computers this way, and that many teachers and professors teach that this is the correct way to handle it. I feel strongly that the convention is wrong. I disagree with some of the statements that have been made defending the convention. And I disagree with some of the statement made by people who disagree with the convention, too. I particularly disagree with the whole "written as" thing, because notational equivalence is not the same as mathematical equivalence, and that's the issue that causes the whole misunderstanding in the first place.

I would enjoy reading your analysis of 5^2 - 5^2

 

[bostonfred]

In posts #1381 and #1383, you said that you don't question the existence of the convention [that exponents precede the unary minus in the order of operations] even though the convention doesn't lend itself to clear mathematical convention.

I took that as an acknowledgment that the standard convention is to resolve the exponent before the unary minus, such that -5^2 = -25. Are you changing your mind? Or did I misunderstand your previous posts?

I think you've understood correctly. I feel strongly that the standard is wrong. There is an unambiguously correct way to read -5^2, but I acknowledge the existence of an agreed-upon convention among many in the mathematical community. The existence of this convention causes ambiguity, because I will never know if I am communicating with is right minded like me or simply following the incorrect convention, and thus I will always be forced to put parentheses around things that don't need them, and to ask what someone means when they don't use parentheses. It is what it is.

 

[Chaka]

Cheese and crackers.

If a discussion comes up about fractions, Joe is going to have to open a new website.

Fractionguys.com®

It's 'Crackers and cheese' bub.

 

[bostonfred]

I would enjoy reading your analysis of 5^2 - 5^2

This isn't difficult unless you get confused by that little dash that's hovering midway through the equation. 5^2 - 5^2 = 0. we can show this as -x = 0is the notational (and mathematical) equivalent of x + -(x) = 0Replacing x with 5^2, we get 5^2 - (5^2) = 0Note that 5^2 - 5^2 is NOT the notational equivalent of -5^2 + 5^2. The answer to the latter should* be 50. * clarifying for Maurile that I understand that calculators and poor students of math will disagree because they've agreed upon a convention to the contrary

 

[Short Corner]

5 + -5^2 = what?

Slight spinoff, as I was helping my step daughter with her homework the other day. Is this a apprpriate way to write an equation? Obviously you are not including parens to make a point. However, my step daughter will write answers to her homework like this:y = x + - 6which I tell her is incorrect, and that you should write it:y = x - 6to which she says her teacher doesn't care, and doesn't mark it wrong. This isn't an acceptable form of an equation, is it?

Both are acceptable.

 

[Mr. Pickles]

>> -5^2

ans =

-25

MATLAB knows.

 

[Maurile Tremblay]

In posts #1381 and #1383, you said that you don't question the existence of the convention [that exponents precede the unary minus in the order of operations] even though the convention doesn't lend itself to clear mathematical convention.

I took that as an acknowledgment that the standard convention is to resolve the exponent before the unary minus, such that -5^2 = -25. Are you changing your mind? Or did I misunderstand your previous posts?

I think you've understood correctly. I feel strongly that the standard is wrong. There is an unambiguously correct way to read -5^2, but I acknowledge the existence of an agreed-upon convention among many in the mathematical community. The existence of this convention causes ambiguity, because I will never know if I am communicating with is right minded like me or simply following the incorrect convention, and thus I will always be forced to put parentheses around things that don't need them, and to ask what someone means when they don't use parentheses. It is what it is.

Fair enough.

 

[Maurile Tremblay]

>> -5^2ans = -25MATLAB knows.

Excel agrees with this as well, at least from within the VBA editor.In Excel, if you type "=-5^2" in a cell, you get 25.But if you type "print -5^2" in the immediate window in the VBA editor, it returns -25.

 

[bostonfred]

>> -5^2ans = -25MATLAB knows.

Excel agrees with this as well, at least from within the VBA editor.In Excel, if you type "=-5^2" in a cell, you get 25.But if you type "print -5^2" in the immediate window in the VBA editor, it returns -25.

more ambiguity created by this so-called convention

 

[Ilov80s]

I would enjoy reading your analysis of 5^2 - 5^2

This isn't difficult unless you get confused by that little dash that's hovering midway through the equation. 5^2 - 5^2 = 0. we can show this as -x = 0is the notational (and mathematical) equivalent of x + -(x) = 0Replacing x with 5^2, we get 5^2 - (5^2) = 0Note that 5^2 - 5^2 is NOT the notational equivalent of -5^2 + 5^2. The answer to the latter should* be 50. * clarifying for Maurile that I understand that calculators and poor students of math will disagree because they've agreed upon a convention to the contrary

Why isn't it the equivalent? 5-3= -3 + 5 How come that doesn't hold true in your scenario?

 

[LarryAllen'sJockstrap]

>> -5^2ans = -25MATLAB knows.

Excel agrees with this as well, at least from within the VBA editor.In Excel, if you type "=-5^2" in a cell, you get 25.But if you type "print -5^2" in the immediate window in the VBA editor, it returns -25.

more ambiguity created by this so-called convention

Using the Excel "=" function, this is what is produced for the following scenarios:"= -(5^2)" = -25"= (-5)^2" = 25"= -5^2" = 25I'm not arguing one way or the other; just sayin...

 

[boubucarow]

I see the point bostonfred is making. I think the problem lies in that fact that originally there were only positive numbers. So although a negative number is technically an integer which is the simplest form, they were seen as a negative of a positive number.

I was strongly in the -25 camp and now I am not so sure. And I don't care what most people think if they can't prove it.

 

[Short Corner]

Seriously, 29 pages on this? -5^2 = -25

-5^2 = 25

Nope, put it into a scientific calculator and you will see you are wrong.

Excel says it is 25. More people use Excel for calculations everyday than use a scientific calculator in a year. Since we are talking about a language, it is the translation of that language that is generally understood by the people who speak the language that matters.Microsoft and I say 25.

Excel has implied parens so what you are really calculating is (-5)^2

 

[Short Corner]

-5 cannot be "written as" -1*5. There's no such thing as "written as".

"Written as" is a synonym for "expressed as."For any given number, there are numerous way to express it. Negative five can be expressed as "-5" or "(-1)*5" or any other number of ways.

-5 cannot be expressed as (-1)*5.

It can be expressed an infinite number of ways.

 

[bostonfred]

I would enjoy reading your analysis of 5^2 - 5^2

This isn't difficult unless you get confused by that little dash that's hovering midway through the equation. 5^2 - 5^2 = 0. we can show this as -x = 0is the notational (and mathematical) equivalent of x + -(x) = 0Replacing x with 5^2, we get 5^2 - (5^2) = 0Note that 5^2 - 5^2 is NOT the notational equivalent of -5^2 + 5^2. The answer to the latter should* be 50. * clarifying for Maurile that I understand that calculators and poor students of math will disagree because they've agreed upon a convention to the contrary

Why isn't it the equivalent? 5-3= -3 + 5 How come that doesn't hold true in your scenario?

Again, not difficult. I agree that: x-y = -y + x This is because -y is the notational equivalent of (-1). However, (-1)(5^2) is not the notational equivalent of -5^2. If you'd like a detailed explanation of the reason why they are not the same, please reread my previous posts on the matter. I've been fairly clear about it, but I'd be happy to answer specific questions.

 

[Maurile Tremblay]

I think the problem lies in that fact that originally there were only positive numbers.

That's going back before World War II, right?

 

[jon_mx]

>> -5^2ans = -25MATLAB knows.

Excel agrees with this as well, at least from within the VBA editor.In Excel, if you type "=-5^2" in a cell, you get 25.But if you type "print -5^2" in the immediate window in the VBA editor, it returns -25.

more ambiguity created by this so-called convention

Using the Excel "=" function, this is what is produced for the following scenarios:"= -(5^2)" = -25"= (-5)^2" = 25"= -5^2" = 25I'm not arguing one way or the other; just sayin...

but =0-5^2 = -25....which is why i say it is ambiguous and depends upon the context. As a stand alone number, -5^2 is 25. But embedded in an equation as an operation it represents -25. That is the problem with the "-" sign in math. It is the same symbol for two different concepts, a negative and a minus. Not always the same outcome.

 

[Short Corner]

I think the problem lies in that fact that originally there were only positive numbers.

That's going back before World War II, right?

:(

 

[Ilov80s]

I would enjoy reading your analysis of 5^2 - 5^2

This isn't difficult unless you get confused by that little dash that's hovering midway through the equation. 5^2 - 5^2 = 0. we can show this as -x = 0is the notational (and mathematical) equivalent of x + -(x) = 0Replacing x with 5^2, we get 5^2 - (5^2) = 0Note that 5^2 - 5^2 is NOT the notational equivalent of -5^2 + 5^2. The answer to the latter should* be 50. * clarifying for Maurile that I understand that calculators and poor students of math will disagree because they've agreed upon a convention to the contrary

Why isn't it the equivalent? 5-3= -3 + 5 How come that doesn't hold true in your scenario?

Again, not difficult. I agree that: x-y = -y + x This is because -y is the notational equivalent of (-1). However, (-1)(5^2) is not the notational equivalent of -5^2. If you'd like a detailed explanation of the reason why they are not the same, please reread my previous posts on the matter. I've been fairly clear about it, but I'd be happy to answer specific questions.

You are just picking and choosing here. The - infront of x should not be considered any different than the - infront of x^2.

 

[boubucarow]

I think the problem lies in that fact that originally there were only positive numbers.

That's going back before World War II, right?

:(

Yeah, it goes way back. The question here is whether or not -5 is in its simplest expression. Those stating the answer is -25 are saying it is not. So that means that integers are not the simplest expression. Then only natural numbers are the simplest expression. Unless you can tell me why an integer isn't the simplest expression, I have to think the history of numbers are what influenced the treatment of such a problem.

 

[bostonfred]

I see the point bostonfred is making. I think the problem lies in that fact that originally there were only positive numbers. So although a negative number is technically an integer which is the simplest form, they were seen as a negative of a positive number.I was strongly in the -25 camp and now I am not so sure. And I don't care what most people think if they can't prove it.

That's close. It's not that there were originally only positive numbers. It's that we decided on a poor naming convention for negative numbers. Calling a number -2 is shorthand for the number that is two less than zero, but the number that is two less than zero is a meaningful constant just like the number two greater than zero is. We just choose to call it -2 because it's an easier concept for people to learn. -2 is equal to zero minus two. That's easy to learn. -2 plus 3 is equal to three minus two. Look how simple negative numbers are to learn if you just put a minus sign in front of their absolute value. And we must be able to do math on all constants, including ones that are less than zero. We have meaningful rules for them, like the rule that a negative number times another negative number equals a positive number. We use absolute values to measure the "distance" from zero. Having a minus sign is pretty easy for stuff like that and doesn't cause much confusion. So why wouldn't we treat the constant known as -5 as a separate entity upon which math can be performed? There is no operation happening here. We didn't have to call it minus five, we just happened to do so because it made the concept of negative numbers easier for people to learn and perform operations on. If we'd called it Grolokowicz instead of -5, then the idea of Grolokowicz^2 would be unambigous. It's a shame that we had to dumb down our mathematical expression to make it learnable for people who are not good at math, to the point of confusing the people who are good at math, but the tradeoff is probably a fair one. We end up with poor conventions that cause ambiguity.

 

[bostonfred]

You are just picking and choosing here. The - infront of x should not be considered any different than the - infront of x^2.

However, (-1)(5^2) is not the notational equivalent of -5^2. If you'd like a detailed explanation of the reason why they are not the same, please reread my previous posts on the matter. I've been fairly clear about it, but I'd be happy to answer specific questions.

If x = 5, -x^2 = -25.

However, -5^2 =25, NOT -25.

If this is true, then the burden on me is to prove why -x is distinct from -5 if they both have a minus in front of them. I am doing so by showing that -x and -5 are different in the same way that 2x and 25 are different and -1x and -1x are different. The minus sign has a different meaning when placed in front of a variable than when placed in front of a number.

A minus sign in front of a number is an adjective. It's a way of describing a complete concept. A minus sign in front of a variable is an operation. It's a way of describing the number by which we multiply the variable.

You may replace -5 with (-1*5) or even ((-1)*(5)) if you prefer. But you can't replace it without using parentheses around it, anymore than you can replace it with 17-22 without using parentheses.

 

[boubucarow]

I see the point bostonfred is making. I think the problem lies in that fact that originally there were only positive numbers. So although a negative number is technically an integer which is the simplest form, they were seen as a negative of a positive number.I was strongly in the -25 camp and now I am not so sure. And I don't care what most people think if they can't prove it.

That's close. It's not that there were originally only positive numbers. It's that we decided on a poor naming convention for negative numbers. Calling a number -2 is shorthand for the number that is two less than zero, but the number that is two less than zero is a meaningful constant just like the number two greater than zero is. We just choose to call it -2 because it's an easier concept for people to learn. -2 is equal to zero minus two. That's easy to learn. -2 plus 3 is equal to three minus two. Look how simple negative numbers are to learn if you just put a minus sign in front of their absolute value. And we must be able to do math on all constants, including ones that are less than zero. We have meaningful rules for them, like the rule that a negative number times another negative number equals a positive number. We use absolute values to measure the "distance" from zero. Having a minus sign is pretty easy for stuff like that and doesn't cause much confusion. So why wouldn't we treat the constant known as -5 as a separate entity upon which math can be performed? There is no operation happening here. We didn't have to call it minus five, we just happened to do so because it made the concept of negative numbers easier for people to learn and perform operations on. If we'd called it Grolokowicz instead of -5, then the idea of Grolokowicz^2 would be unambigous. It's a shame that we had to dumb down our mathematical expression to make it learnable for people who are not good at math, to the point of confusing the people who are good at math, but the tradeoff is probably a fair one. We end up with poor conventions that cause ambiguity.

Obviously, you stated it much better and correctly than I. So you think -5 is treated like two separate entities simply because we have no way of expressing it in one entity, correct? Does that also account for why the majority of mathematicians see -25?

 

[videoguy505]

-5 cannot be "written as" -1*5. There's no such thing as "written as".

"Written as" is a synonym for "expressed as."For any given number, there are numerous way to express it. Negative five can be expressed as "-5" or "(-1)*5" or any other number of ways.

-5 cannot be expressed as (-1)*5.

It can be expressed an infinite number of ways.

I remember the day when my mind was blown when I first learned that "0.9999999..... (infinitely repeating)" is the same as "1".

 

[bostonfred]

I see the point bostonfred is making. I think the problem lies in that fact that originally there were only positive numbers. So although a negative number is technically an integer which is the simplest form, they were seen as a negative of a positive number.I was strongly in the -25 camp and now I am not so sure. And I don't care what most people think if they can't prove it.

That's close. It's not that there were originally only positive numbers. It's that we decided on a poor naming convention for negative numbers. Calling a number -2 is shorthand for the number that is two less than zero, but the number that is two less than zero is a meaningful constant just like the number two greater than zero is. We just choose to call it -2 because it's an easier concept for people to learn. -2 is equal to zero minus two. That's easy to learn. -2 plus 3 is equal to three minus two. Look how simple negative numbers are to learn if you just put a minus sign in front of their absolute value. And we must be able to do math on all constants, including ones that are less than zero. We have meaningful rules for them, like the rule that a negative number times another negative number equals a positive number. We use absolute values to measure the "distance" from zero. Having a minus sign is pretty easy for stuff like that and doesn't cause much confusion. So why wouldn't we treat the constant known as -5 as a separate entity upon which math can be performed? There is no operation happening here. We didn't have to call it minus five, we just happened to do so because it made the concept of negative numbers easier for people to learn and perform operations on. If we'd called it Grolokowicz instead of -5, then the idea of Grolokowicz^2 would be unambigous. It's a shame that we had to dumb down our mathematical expression to make it learnable for people who are not good at math, to the point of confusing the people who are good at math, but the tradeoff is probably a fair one. We end up with poor conventions that cause ambiguity.

Obviously, you stated it much better and correctly than I. So you think -5 is treated like two separate entities simply because we have no way of expressing it in one entity, correct? Does that also account for why the majority of mathematicians see -25?

Mathematicians are lazy by nature and have given in to peer pressure on this. If I had to guess why, it's because it's easier to build rules into a calculator when you can replace any number with an x, simplify the calculation, then replace the x with the number and finish it. And it's easier to build a calculator that treats 5 as x and -5 as -x than to treat -5 as x.

 

[Short Corner]

The minus sign has a different meaning when placed in front of a variable than when placed in front of a number. A minus sign in front of a number is an adjective. It's a way of describing a complete concept. A minus sign in front of a variable is an operation. It's a way of describing the number by which we multiply the variable.

This is incorrect. The minus sign has the exact same meaning for both of these expressions. It basically means 'the opposite of'.

 

[bostonfred]

The minus sign has a different meaning when placed in front of a variable than when placed in front of a number. A minus sign in front of a number is an adjective. It's a way of describing a complete concept. A minus sign in front of a variable is an operation. It's a way of describing the number by which we multiply the variable.

This is incorrect. The minus sign has the exact same meaning for both of these expressions. It basically means 'the opposite of'.

You're absolutely -right.

 

[Short Corner]

Mathematicians are lazy by nature and have given in to peer pressure on this. If I had to guess why, it's because it's easier to build rules into a calculator when you can replace any number with an x, simplify the calculation, then replace the x with the number and finish it. And it's easier to build a calculator that treats 5 as x and -5 as -x than to treat -5 as x.

Originally calculators were spitting out 25. If mathematicians are a lazy bunch, why did they go through the trouble of changing it to give the incorrect (according to you) answer. The convention was also in place hundreds of years before the first calculator FWIW.

 

[Short Corner]

The minus sign has a different meaning when placed in front of a variable than when placed in front of a number. A minus sign in front of a number is an adjective. It's a way of describing a complete concept. A minus sign in front of a variable is an operation. It's a way of describing the number by which we multiply the variable.

This is incorrect. The minus sign has the exact same meaning for both of these expressions. It basically means 'the opposite of'.

You're absolutely -right.

You really got me there.

 

[Hooper31]

It is clearly not universally accepted, see this thread.

To say there is "clearly" not a universally accepted convention is just wrong. This is akin to a person standing outside on a sunny day pointing at the sky claiming that is actually raining constitutes enough of an opposition to argue against a universal convention of what precipitation means.If you put 1000 random high school and college mathematics professors in a room you're going to find a few of them that will argue that there is some ambiguity while the other 990+ just sort of roll their eyes into their heads wondering why anyone would bother wasting time with the argument.

I didn't realize that question was directed at me. Do mathematicians have a national association?

There are many national and worldwide associations of mathematicians. Currently I belong to the NCTM and I routinely participate in the forums at Drexel University. One of the popular forums there is Ask Dr. Math. This same discussion has taken place many times. Yes, there are a few holdouts that argue against the convention just like you will find in any other arena, but the reality is that the overwhelming majority of professionals in the mathematics field agree on the convention.

Your definition of universal is really weird. Not everyone accepts the convention if there are holdouts even among mathematicians.

To be more clear, those same mathematicians would fall in line if their lives depended on it. What I was trying to explain above is that there are going to be a small number of holdouts that will argue just for the sake of arguing. Even the dissidents know what the convention is and can easily explain why there is a need for the understood convention. I doubt there are many high school math teachers that haven't had this same back and forth on the subject. I understand why the discussion takes place. In my opinion one of the main causes for it occurring is the keyboard right in front of you. Often I see people represent their minus signs in a different way than the way they show a negative number. The negatives are sometimes represented with a smaller raised symbol. I think its possible to do this on the keyboard, but I'm not entirely sure how, and its not one of the main keystrokes. I think someone in this very thread used that symbol once. Just more food for thought.

 

[bostonfred]

Mathematicians are lazy by nature and have given in to peer pressure on this. If I had to guess why, it's because it's easier to build rules into a calculator when you can replace any number with an x, simplify the calculation, then replace the x with the number and finish it. And it's easier to build a calculator that treats 5 as x and -5 as -x than to treat -5 as x.

Originally calculators were spitting out 25. If mathematicians are a lazy bunch, why did they go through the trouble of changing it to give the incorrect (according to you) answer. The convention was also in place hundreds of years before the first calculator FWIW.

The original calculators were developed by mathematicians trying to be a beacon of light and truth in an unjust mathematical world. Those were simpler times. The more complex calculators are developed by computer programmers trying to understand the requirements given to them by mathematicians, then QA'ed by people who chose to make a living testing mathematical equations plugged into a computer program so they can see if it gives them the answer they think is right. There's a lot of people with poor communication skills and at least a half dozen people who own a cat shirt involved in this process.

 

[Hooper31]

Using the Excel "=" function, this is what is produced for the following scenarios:

"= -(5^2)" = -25

"= (-5)^2" = 25

"= -5^2" = 25

I'm not arguing one way or the other; just sayin...

Once upon a time I believe that typing "-5^2" into google also returned 25. That appears to be fixed now. LINK

 

[Psychopav]

HI bf. Long time listener, first time caller.I was wondering why you have been neglecting the exponent on your variable.When you say something like:

If x = 5, -x^2 = -25,However, -5^2 =25, NOT -25.

I wonder how you would answer this question:If x = 5, what does x^-2 equal?orIf x = 5, what does -x^-2 equal?I'll hang up and listen.

 

[jon_mx]

I think the problem lies in that fact that originally there were only positive numbers.

That's going back before World War II, right?

Goes back to the third grade for me. Teacher insisted it was 'impossible' to subtract 5 from 3. It was a lost cause.

 

[Maurile Tremblay]

I remember the day when my mind was blown when I first learned that "0.9999999..... (infinitely repeating)" is the same as "1".

There are a number of proofs for that; here's a simple one that's kind of cool.It should be evident that 0.999999... is equal to 9 * 0.111111....Ever since the invention of calculators, we've known that 1/9 is equal to 0.111111....Since 9 * 1/9 = 1, and since 0.999999... is 9 * 1/9, it must also be true that 0.999999... = 1.

 

[Ilov80s]

The minus sign has a different meaning when placed in front of a variable than when placed in front of a number. A minus sign in front of a number is an adjective. It's a way of describing a complete concept. A minus sign in front of a variable is an operation. It's a way of describing the number by which we multiply the variable.

This is incorrect. The minus sign has the exact same meaning for both of these expressions. It basically means 'the opposite of'.

You're absolutely -right.

and since 5^2 is 25, the opposite of that is -25.

 

[bostonfred]

The minus sign has a different meaning when placed in front of a variable than when placed in front of a number. A minus sign in front of a number is an adjective. It's a way of describing a complete concept. A minus sign in front of a variable is an operation. It's a way of describing the number by which we multiply the variable.

This is incorrect. The minus sign has the exact same meaning for both of these expressions. It basically means 'the opposite of'.

You're absolutely -right.

and since 5^2 is 25, the opposite of that is -25.

Pretty sure you're still having trouble with - signs.

 

[videoguy505]

I can't tell, is fred shticking it up in here, or is he serious? Ever since Dawn/Don, I can't tell when he's wrong and when he's just pretending to be wrong.

 

[boubucarow]

I remember the day when my mind was blown when I first learned that "0.9999999..... (infinitely repeating)" is the same as "1".

There are a number of proofs for that; here's a simple one that's kind of cool.It should be evident that 0.999999... is equal to 9 * 0.111111....Ever since the invention of calculators, we've known that 1/9 is equal to 0.111111....Since 9 * 1/9 = 1, and since 0.999999... is 9 * 1/9, it must also be true that 0.999999... = 1.

That still trips me out to this day.

 

[jon_mx]

The minus sign has a different meaning when placed in front of a variable than when placed in front of a number. A minus sign in front of a number is an adjective. It's a way of describing a complete concept. A minus sign in front of a variable is an operation. It's a way of describing the number by which we multiply the variable.

This is incorrect. The minus sign has the exact same meaning for both of these expressions. It basically means 'the opposite of'.

You're absolutely -right.

You really got me there.

Just lucky he did not -right^2 you

 

[Short Corner]

I remember the day when my mind was blown when I first learned that "0.9999999..... (infinitely repeating)" is the same as "1".

There are a number of proofs for that; here's a simple one that's kind of cool.It should be evident that 0.999999... is equal to 9 * 0.111111....Ever since the invention of calculators, we've known that 1/9 is equal to 0.111111....Since 9 * 1/9 = 1, and since 0.999999... is 9 * 1/9, it must also be true that 0.999999... = 1.

Can you 'prove' 1 = 2?

 

[bostonfred]

1/10 .1

1/100 is .01

1/infinity is .00000...1

1/infinity plus .99999... = 1

therefore 1/infinity = 0

therefore 0 * infinity = 1

therefore 1/0 = infinity

 

[tommyboy]

at some point the convention of -5^2 was accepted that it is -(5^2)?

as opposed to (-5)^2?...

when did that become the convention out of curiosity?

 

[bostonfred]

I can't tell, is fred shticking it up in here, or is he serious? Ever since Dawn/Don, I can't tell when he's wrong and when he's just pretending to be wrong.

Deadly serious. I understand the convention, and I believe it's clearly wrong and creates ambiguity. They should have gone the other way when deciding on a convention.