The Math Lovers Club v. 3.1416

[Sir GuitarCozmo]

Ahh, okay.  Got it.  Thanks!

[Orbert]

The problem is that the question doesn't make any sense.  He's being asked to write an absolute value inequality for a real-world situation which has nothing to do with absolute value.  All weights in this scenario are positive values, so there is no need for absolute value bars anywhere.  He put them around the variable in a desperate attempt to meet the requirements of the question.

I would have no idea how to answer such a stupid question, and I was an algebra teacher.  First thing I thought of was putting bars around the x, just as your son did, and the second thing I thought of was that that is probably going to get marked wrong anyway.

[wasteland]

Something like |x-156|<=4? 156 is the middle point of the given interval, so whatever weight fitting the initial description wouldn't fall farther from the middle point than half of the interval width.

[rumborak]

The problem is that the question doesn't make any sense.  He's being asked to write an absolute value inequality for a real-world situation which has nothing to do with absolute value.  All weights in this scenario are positive values, so there is no need for absolute value bars anywhere.  He put them around the variable in a desperate attempt to meet the requirements of the question.

I would have no idea how to answer such a stupid question, and I was an algebra teacher.  First thing I thought of was putting bars around the x, just as your son did, and the second thing I thought of was that that is probably going to get marked wrong anyway.

I interpreted the "absolute" to refer to that the inequality would include actual, i.e. absolute values.
And, I disagree with that "x" and "|x|" should be both treated as correct because negative weights would make no sense in this scenario. The point of the exercise is in deriving an accurate equation.

[RuRoRul]

Something like |x-156|<=4? 156 is the middle point of the given interval, so whatever weight fitting the initial description wouldn't fall farther from the middle point than half of the interval width.

I think this would be correct. But there's no real way to know what they were looking for, at least without more context - if the material / assignment included trying to learn the meaning of the absolute value symbol and how to write inequalities in terms like the one above then I think wasteland said the right answer. But if it wasn't clear that that sort of thing should be in the assignment and "absolute value inequality" is just some teacher's failed attempt to communicate some other sort of requirements then there's no way to know what they were looking for.

Anyway, assuming it's at least feasible for it to be in the assignment, I would say the answer is as wasteland said, expressing an interval somewhere on the real line as a distance from the midpoint.

[Sir GuitarCozmo]

If context provides any assistance, the quiz page in question is the LAST page of this file:

https://www.westex.org/cms/lib6/NJ01001533/Centricity/Domain/11/Algebra%2011%20Summer%20Packet%202014.pdf

[Orbert]

The problem is that the question doesn't make any sense.  He's being asked to write an absolute value inequality for a real-world situation which has nothing to do with absolute value.  All weights in this scenario are positive values, so there is no need for absolute value bars anywhere.  He put them around the variable in a desperate attempt to meet the requirements of the question.

I would have no idea how to answer such a stupid question, and I was an algebra teacher.  First thing I thought of was putting bars around the x, just as your son did, and the second thing I thought of was that that is probably going to get marked wrong anyway.

I disagree with that "x" and "|x|" should be both treated as correct because negative weights would make no sense in this scenario. The point of the exercise is in deriving an accurate equation.

I never said that they were both correct.  I only said that a proper interpretation of the problem would not involve absolute value, because all values involved in this situation are positive, and everyone knows that.  The problem would be fine for inequalities, number lines, even set theory if you wanted to try hard enough, but not absolute value.

As a brain exercise, I kinda like it.  wasteland has a correct answer, in that the difference between the weight and 156 cannot exceed 4.  The difference between the endpoints is 8, so 156 is in the middle, and you can come up "|x-156|<=4" from there.  Or "|156-x|<=4".

When I wrote application problems, I always felt that it was important to use situations that were appropriate for the type of equation (or inequality, as the case may be) we were studying.

As an inequality, this is a fine problem.  I would go with "152 <= x <= 160" because even though Cozmo's solution is technically correct, we must also consider the convention that you go from least to greatest value, left to right.  But either way.  The important part is to not just slap absolute value bars on the x because that allows for the guy to weigh -156 which makes no sense.  That's really what I was getting at.  This is not a problem that calls for absolute value.  Twisting it around to make it an absolute value inequality is an interesting brain exercise, but completely contrived.

[Jamesman42]

Wait. How would |x - 156|<=4 allow for negative values? It becomes written as 152 <= x <= 160. x is only between those two numbers, inclusively.

Plugging in any negative number into it makes the statement untrue. Or am I missing something too obvious?

Seems like the problem is seeing if you can a) write it as a normal compound inequality and b) THEN take that and compact it into an absolute value inequality. I like the question, gets you into thinking about reversing the process when usually students learn to "undo" the absolute value sign (at least where I am from).

[rumborak]

Something <= |x| <= something

Allows for negative values. That's what the kid wrote down.

[Jamesman42]

Oh, you were talking about what the kid wrote down. My bad

[jasc15]

So i've heard about The Curta Calculator but never seen one or really gave it any deep thought on how complicated it really is. Here's a nice little video demononstration:

https://www.youtube.com/watch?v=P0cGjC62XRQ

A genious invention!

Here's another video:

https://www.youtube.com/watch?v=ZDn_DDsBWws

and a simulation:

https://www.curta.de/kr34/curta_simulator_en.htm

I've wanted one of these since I first read about it in a scientific american magazine about 12 years ago.  Unfortunately, they go for about $1000 or so on ebay.



For now, I'll have to remain happy with my K&E Deci-Lon slide rule

[DarkLord_Lalinc]

I love Math.






Even more than I love Physic.

Your english humor won't impress me.




You should considre changing your ways.

[MrBoom_shack-a-lack]

An intellectually challenging game of loop

Would love to play a round of loop.

[BlobVanDam]

I saw a few videos about it a little while ago on Numberphile and thought it was really awesome. I wonder if they could do anything to get it working more reliably, or whether that's the best it will get in practice.

[Onno]

That's really cool!

[Chino]

https://www.newscientist.com/article/2073909-prime-number-with-22-million-digits-is-the-biggest-ever-found/

It’s time for a new prime to shine. The largest known prime number is now 274,207,281 – 1, smashing the previous record by nearly 5 million digits.

This mathematical monster was discovered by Curtis Cooper at the University of Central Missouri in Warrensburg as part of the Great Internet Mersenne Prime Search (GIMPS), a collaborative effort to find new primes by pooling computing power online. It has 22,338,618 digits in total.

[cramx3]

I was wondering what the point was of doing this so I read the article... and there is no point 

[Orbert]

Correct!  Number geeks get off on numbers, and finding the largest prime is about as number-geeky as you can get.  Since there is no "largest prime of all" (you could theoretically go on infinitely), the prize goes to the "largest known prime".  A prime number with 22 million digits?  There are at least a few math geeks who literally had to change their underwear after hearing that.

[DT_12_Octavarium]

Did you know that 0.99999 = 1. It seems nonsensical but it's true

[EraVulgaris]

Did you know that 0.99999 = 1. It seems nonsensical but it's true

It's one of those things were the decimal representation of a number doesn't seem to be 100% correct, although it is. If we consider that 0.333.... can be expressed as a fraction (which would be 1/3), it suddenly makes complete sense because

1/3*3 = 1

thus

0.333.... * 3 = 0.999.... = 1

[ariich]

Technically 0.99999 does not equal 1, it equals 0.99999.

However, 0.99 recurring, i.e. 0.999999999999999999999999999999999 and an infinite number of further 9s, that equals 1.

[Orbert]

Did you know that 0.99999 = 1. It seems nonsensical but it's true

No, it's not.  0.99999 is finite.  You meant 0.99999...

The difference is that the ellipsis indicates that the nines go on forever.  If they literally go on forever, the value approaches 1.0 by a smaller and smaller margin with each digit.  Since the nines do go on infinitely, the margin of difference, by definition, becomes infinitesimally small.


Ninja'd, but whatever.

[Prog Snob]

Exactly.  0.99999... will never be 1.0

[Orbert]

"will never be"?  No, it actually is.  Mathematical definition of a limit.

[Prog Snob]

Expound on that.

[Jamesman42]

Well, in laymen's terms, there is no "space" on the real number line between 0.999... and 1. Ask yourself this: What is the difference (subtraction) between 1 and 0.999...?

[Prog Snob]

Well, in laymen's terms, there is no "space" on the real number line between 0.999... and 1. Ask yourself this: What is the difference (subtraction) between 1 and 0.999...?

.001

[Jamesman42]

You do know the "..." means the 9's keep going, right?

[Prog Snob]

Yes. So you're saying there is no right answer to that equation?

[cramx3]

0.9999... = 1

0.99999 /= 1

[Prog Snob]

So then there's some logical explanation as to why that's the case I assume?

[CDrice]

So then there's some logical explanation as to why that's the case I assume?

Did you know that 0.99999 = 1. It seems nonsensical but it's true

It's one of those things were the decimal representation of a number doesn't seem to be 100% correct, although it is. If we consider that 0.333.... can be expressed as a fraction (which would be 1/3), it suddenly makes complete sense because

1/3*3 = 1

thus

0.333.... * 3 = 0.999.... = 1

At least that's the way I understand it.

[cramx3]

The fraction example makes perfect sense. 

When I think about it I think about infinity, the ... representing the 9s going on infinitely and the gap between 0.999.. and 1 becomes infinitely small where it can be considered 0.  Essentially reworded what Orbert said.

DT_12_Octavarium is a troll just trying to stir the pot of minds that like to discuss these details.

[Prog Snob]

It makes perfect sense when you look at it that way. 

[Prog Snob]

Oh, and this is for the troll.