48÷2(9+3) = 2 or 288??!?!?!

[Mini Mic]

http://knowyourmeme.com/memes/48293

 

[T-block]

No, it's not undefined. The answer IS 6. It EQUALS 6. You can use basic algebra to reduce the fraction to (x+3). Just like you can use basic algebra to multiply .999... by 10 and subtract .999... and divide by 9 to equal 1. Duh.

Wrong.

You can only reduce the fraction for x not equal to 3. When x = 3, reducing by x-3 involves dividing by zero. Do I have to explain to you why that's not allowed?

The simplified form of (x+3) is equivalent to (x²-9)/(x-3) for all x not equal to 3. However, at x=3, the functions are describing two very different things.

 

[Elyssa Xey Hexen]

Wrong.

You can only reduce the fraction for x not equal to 3. When x = 3, reducing by x-3 involves dividing by zero. Do I have to explain to you why that's not allowed?

The simplified form of (x+3) is equivalent to (x²-9)/(x-3) for all x not equal to 3. However, at x=3, the functions are describing two very different things.

Its funny though that when taking limits in mathematics you do exactly this. You divide by a zero value to obtain a simplified verision of equation, plug the value into the simplified form and achieve the value at which x approaches some constant. (Or in this case, x approaches 3)

 

[eighteenspikes]

Its funny though that when taking limits in mathematics you do exactly this. You divide by a zero value to obtain a simplified verision of equation, plug the value into the simplified form and achieve the value at which x approaches some constant. (Or in this case, x approaches 3)

Right, the limit as you approach 3 converges to 6. Similarly, the infinite series of .999... converges to 1. But it doesn't equal 1. Wikipedia even says this, and you would know that if you ever took a pre-calc course, Ocean. Cough.

 

[Vinylic.]

This is where it's all been leading too....

 

[Fuelbi]

You know, like squared numbers, number "to the power of _" ect

Oh you mean exponents lol


Man are you guys SERIOUSLY arguing a Wiki article? Come on, if you do an argument based on an article, at least pick one that's accepted and not full of 12 year olds with nothing to do in their lives so they screw up wiki articles for fun

 

[ballin4life]

Sometimes I wonder if majoring in Math is a good route, and then I see topics like these and feel a lot more reassured.

lol this has NOTHING to do with being a math major ... ill formed arithmetic expressions aren't really in the curriculum


Also guys, it's either PEDMSA (division before multiplication and subtraction before addition), or PEMA (recognizing that multiplication is the same as division and subtraction is the same as addition).

PEMDAS is going to mess you up unless you realize that multiplication is the same as division and subtraction is the same as addition (which isn't obvious from the acronym).

 

[Elyssa Xey Hexen]

PEMDAS is going to mess you up unless you realize that multiplication is the same as division and subtraction is the same as addition (which isn't obvious from the acronym).

Say we have some constant number "a", and put that into some generic f(x) and get a constant number "b" in return. If we put "b" into some other function--let's say g(x)--, and we get the constant number "a" back.

This tells us that f(x) and g(x) are inverse functions of each other.

Addition and subtraction are inverse functions of each other, and the same with multiplication and divison. So, as ballin4life said, the actual order of multiplication or divison does not really matter so long as those are the only operations involved and the same with addition and subtraction.

Also, for anyone who is remembering trigonometry. sin(x) & arcsin(x) are inverse operations of each other (the same for tan & arctan and cos & arccos).

So,
sin(pi/2) = {sqrt(2)/2}
arcsin{sqrt(2)/2} = pi/2

Inverse operations undo each other :D

 

[Cathy]

Right, the limit as you approach 3 converges to 6. Similarly, the infinite series of .999... converges to 1. But it doesn't equal 1. Wikipedia even says this, and you would know that if you ever took a pre-calc course, Ocean. Cough.

This is really a semantic issue, not a mathematical one, but your distinction between what an infinite series converges to and the value of that series is unusual; generally the definition of the value of an infinite series is the limit of its corresponding sequence of partial sums.

To be more explicit, generally when dealing when real numbers the notation 0.999 denotes the infinite series 0.9+0.09+0.009+..... By the definition of the sum of infinite series, that is equal to the limit of this sequence of "partial sums": { 0.9, 0.9 + 0.09, 0.9 + 0.09 + 0.009, ... }. No entry in the sequence of partial sums is equal to 1, but the limit of the sequence of partial sums is 1, and since the definition of 0.99... = 0.9+0.09+0.009+... is the limit of that sequence, it is equal to 1 (i.e. 0.99 = 1). The standard terminology is to say an infinite series converges if the limit of the corresponding sequence of partial sums exist, but if it does converge, its value is equal to that limit. In other words, when you write the notation "0.99..." that is already invoking a limit; you don't need to take the limit of it to get 1.

I am not sure which Wikipedia article you have in mind (this one perhaps, but it doesn't use your unusual distinction) but you are probably confusing the value of an infinite series (which, if the series converges, equals some number) with the corresponding sequence of partial sums (which may not contain the value of the infinite series at all!). But the reason I said it's a "semantic issue" is that as you an see from my post it really has everything to do with terminology, rather than math, but in the usual terminology, when dealing with real numbers, saying that an infinite series converges to some value is the same thing as saying it equals that value... there is no distinction.

Say we have some constant number "a", and put that into some generic f(x) and get a constant number "b" in return. If we put "b" into some other function--let's say g(x)--, and we get the constant number "a" back.

This tells us that f(x) and g(x) are inverse functions of each other.

Addition and subtraction are inverse functions of each other, and the same with multiplication and divison. So, as ballin4life said, the actual order of multiplication or divison does not really matter so long as those are the only operations involved and the same with addition and subtraction.

Also, for anyone who is remembering trigonometry. sin(x) & arcsin(x) are inverse operations of each other (the same for tan & arctan and cos & arccos).

So,
sin(pi/2) = {sqrt(2)/2}
arcsin{sqrt(2)/2} = pi/2

Inverse operations undo each other :D

Division and multiplication aren't exactly inverses and that fact is kind of the whole point behind some of the earlier posts. Like, the function "multiply by x" and "divide by x" are not inverses of each other, since f(x) = 1 and g(x) = x/x are not the same function (g applies "multiply by x" to 1, followed by applying "divide by x" to the result). g is not defined at x = 0, but f is. The function g is of course continuous though.

Another example of the same thing is that the "multiply by 0" function has no inverse at all. That function takes any number to 0, but that process loses information; there's no way to turn 0 back into the original number. Of course, both of these are actually examples of the same obvious fact, which is that zero does not have a multiplicative inverse.

There's a similar obvious subtlety with the trig example, namely that sine and arcsin are only inverses on a particular subset of the real numbers that you choose, they aren't inverses on the whole real number line because an infinite number of angles have the same sine as each other, but arcsin can only take that sine value back to a single angle.

It is, however, true that altering the order of multiplications does not change the result. That's called "commutativity".

Man are you guys SERIOUSLY arguing a Wiki article? Come on, if you do an argument based on an article, at least pick one that's accepted and not full of 12 year olds with nothing to do in their lives so they screw up wiki articles for fun

In my experience, Wikipedia tends to have pretty excellent math articles.

 

[Vinylic.]

This math question is used for some trolling. It's known as a meme. I'm putting this question on "everybody votes channel."


The real answer could be both of them or none. If none, the real answer is "ignore this question"

 

[1048576]

The real question is whether the convention x(y) should be taken to mean x*y or (x*y)

Eh, what color car do you drive? It doesn't matter as long as it's made clear to the person you're communicating with.

 

[eighteenspikes]

This math question is used for some trolling. It's known as a meme. I'm putting this question on "everybody votes channel."


The real answer could be both of them or none. If none, the real answer is "ignore this question"

my god... we were all masterfully trolled by the thread consisting of the title and "Discuss! ~!!!!!!!" ... I should have known.. but.. it was too subtle...

edit: and what are these mems you speak of?

 

[Vinylic.]

my god... we were all masterfully trolled by the thread consisting of the title and "Discuss! ~!!!!!!!" ... I should have known.. but.. it was too subtle...

edit: and what are these mems you speak of?

If you press here you can learn all about it. and plus, They are both the answers. So there is no need to figure out the "true" answer. Also, you don't need college math or science math or whatever the heck they are because this....this is 5th grade stuff...

BUT, i got a surprise for you.

One more thing, Mini Mic tried to tell you guys about this.

 

[Jolteon]

÷ sucks .

 

[FIREL]

wow........

 

[GunmasterLombardi]

1 / .5 = 2

.999 / .5 = not 2

It's not rocket science gentleman.

 

[~ Gheb ~]

The real answer could be both of them or none.

No, the answer can only be 288. The term (9+3) is not part of the denominator.

 

[Ghostbone]

No, the answer can only be 288. The term (9+3) is not part of the denominator.

Debatable

The implied multiplication of 2(9+3) can be seen to supersede the division, so it may actually be part of the denominator.

Similarly to how 3/2x is generally seen to mean 3 ÷ (2x) not (3 ÷ 2) * x

 

[UltiMario]

This is why I always write my problems with redundant parenthesis, so this never happens.

Like seriously if I was writing this out in my calculator it would be like ****ing.

((48)/(2))(9+3)

It's never a bad thing to put in too many parenthesis!

 

[~ Gheb ~]

Debatable

The implied multiplication of 2(9+3) can be seen to supersede the division, so it may actually be part of the denominator.

In order for it to be part of the denominator it needs to be written within paranthesis:
48 % [2 (9+3)]. The solution to this equation would be 2 because the whole term 2(9 + 3) is the denominator.
Without paranthesis only 2 is part of the denominator, while the term (9+3) is multiplied with the term 48/2 and the result to that is 288.

Similarly to how 3/2x is generally seen to mean 3 ÷ (2x) not (3 ÷ 2) * x

You used a fraction bar, not a division sign. Key difference.

3 % 2 * X = (3/2) * X
3 % (2 * X) = 3/2X

 

[Ganonsburg]

This is why I always write my problems with redundant parenthesis, so this never happens.

Like seriously if I was writing this out in my calculator it would be like ****ing.

((48)/(2))(9+3)

It's never a bad thing to put in too many parenthesis!

I'm glad I'm not the only one who does this. I also do this when conveying math via the internet. It really doesn't hurt to make oneself clear.

 

[Beat!]

1 / .5 = 2

.999 / .5 = not 2

It's not rocket science gentleman.

There's a pretty damn big difference between "0.999" and "0.999...". Try again.

 

[Elyssa Xey Hexen]

Division and multiplication aren't exactly inverses and that fact is kind of the whole point behind some of the earlier posts.

There's a similar obvious subtlety with the trig example, namely that sine and arcsin are only inverses on a particular subset of the real numbers that you choose,

Those subtle rules that we take for granted. Yes, I never defined the interval for which they are inverses.

 

[Deleted member]

to all the nay-sayers:
http://upload.wikimedia.org/math/6/f/a/6fa510b44742046a167b4b8515162825.png

alternatively:
X= 0.999...
10X = 9.999...
10X-X = 9
9X = 9
X = 1

they are even equal by definition:
If 2 real numbers are unequal there exists a (rational) number between them.

 

[Rici]

Yes, let's make up rules when dealing with infinite numbers! Suddenly 2 times infinity = infinity but infinity divided by 2 is not.

I also have a rule. Multiplying something by 10 means there is an 0 behind the original number.
Where is the 0 in 9.999~

Also 'there always exist a number between 2 rational numbers' is a stupid made up axiom.
Just because we can't tell what's between 0,999~ and 1 doesn't make them equal. In olden days before the decimal point, there was nothing between 1 and 2, or 2 and 3 but that didn't make them equal. Just means we didn't have system for it yet. Like now we don't have a system for the numbers between 0.999~ and 1.

 

[eighteenspikes]

to all the nay-sayers:
http://upload.wikimedia.org/math/6/f/a/6fa510b44742046a167b4b8515162825.png

alternatively:
X= 0.999...
10X = 9.999...
10X-X = 9
9X = 9
X = 1

they are even equal by definition:
If 2 real numbers are unequal there exists a (rational) number between them.

That's a limit, baby!

 

[Ocean]

I also have a rule. Multiplying something by 10 means there is an 0 behind the original number.
Where is the 0 in 9.999~

except that's not a rule. there's no zero at the end of 10π either, but that doesn't say anything about π, 10, or anything.

 

[Beat!]

I also have a rule. Multiplying something by 10 means there is an 0 behind the original number.

I'm sorry, what?

 

[Rici]

10 x 2 = 20
10 x 30 = 300
10 x 56 = 560

?

Anyway, I know what I said there was silly, but I just said it to proof a point. You can't equate rational to irrational numbers and before you go"WTF" on that let me explain this.

10 x π equals 10 x π. This much is true
10 x π in rational numbers is approximately 31,4519216 but it will never ever ever ever EQUAL ten times pi, no matter how many decimals you put behind it.

Likewise 10 x 0.999~ is approximately 9.999~ but it will never equal it, like wise 0.999~ will never equal 1.


Like GunmasterLombardi said, it's not rocket science.

 

[eighteenspikes]

just give it a rest rici, these kids love to regurgitate wikipedia articles and cant wrap their heads around the concept of converging limits. they really do think the numbers themselves are equal.

 

[Beat!]

Likewise 10 x 0.999~ is approximately 9.999~ but it will never equal it, like wise 0.999~ will never equal 1.

That's the part where there's disagreement, lol. If 0.999~ equals 1, then 9.999~ does equal 10. You can't just say "it doesn't".

You're basically saying "X is wrong because it's not right".

 

[Ocean]

10 x 2 = 20
10 x 30 = 300
10 x 56 = 560

?

I don't think you understand the difference between a pattern and a rule.

rici, do you not think that .333... is equal to (1/3)?

 

[Deleted member]

just give it a rest rici, these kids love to regurgitate wikipedia articles and cant wrap their heads around the concept of converging limits. they really do think the numbers themselves are equal.

funny I could swear I was a mathematics undergraduate and my teacher taught me this exactly.

you want to take it up with him?

 

[T-block]

Basically, eighteenspikes has a narrower definition of equality. That's all this argument comes down to, as Cathy said.

 

[Ocean]

Basically, eighteenspikes has a narrower definition of equality. That's all this argument comes down to, as Cathy said.

too bad equality isn't subjective, it's objective.

 

[X1-12]

i dont see how 10 x 0.999... Would not equal 9.999...

Surely the idea of 0.9 recurring is that there is an infinite number of 9s. Moving all of the numbers left a decimal place doesnt change the number of 9s after the point, there is still an infinite number of them

It then logically follows that 9.999... Subtract 0.999... is exactly 9, correct?

 

[T-block]

too bad equality isn't subjective, it's objective.

It gets a little grey when we talk about infinity... you can keep adding terms in the geometric series 0.9 + 0.09 + 0.009 + ... and you will never actually reach the value 1.

Of course, with his definition of equality, he's also out of sync with the rest of the mathematical world lol

 

[MK26]

1/3 = .333...
(1/3)*3 = (.333...)*3
1 = .999...

Simple proof

 

[Deleted member]

no that is circular because you assume 1/3 = 0.333... which you can only assume AFTER you have proven 1 = 0.999...

 

[MK26]

^are you serious?

http://www.wolframalpha.com/input/?i=1/3