48÷2(9+3) =

[Orbert]

I see the 2(9+3) as one term, so the implied multiplication does in effect take precedence.

So they'd be separate terms if I made it "2*(9+3)"?

And this seems like a circular argument. Why is it one term? Because implied multiplication takes precedence. Why does implied multiplication take precedence? Because I see it as one term.

If it said 48÷2x = ?  would you divide by 2, then multiply by x?  No, you would find 2x and divide by the result.  Why is 48÷2(9+3) any different?

[MetalManiac666]

288 all up in this bitch.

[Implode]

If it said 48÷2x = ?  would you divide by 2, then multiply by x?  No, you would find 2x and divide by the result.  Why is 48÷2(9+3) any different?

I would ask you to clarify, because the equation is too amboguous.

[rumborak]

I see the 2(9+3) as one term, so the implied multiplication does in effect take precedence.

So they'd be separate terms if I made it "2*(9+3)"?

And this seems like a circular argument. Why is it one term? Because implied multiplication takes precedence. Why does implied multiplication take precedence? Because I see it as one term.

If it said 48÷2x = ?  would you divide by 2, then multiply by x?  No, you would find 2x and divide by the result.  Why is 48÷2(9+3) any different?

What about 48÷2(9+3)(5+3)(2+8) ?
Do you just assume everything after the ÷ sign to be in the denominator? That's a pretty arbitrary decision given multiplication and division are of equal rank.

rumborak

[Orbert]

Yeah, I would.  I always presumed that implied multiplication gave it some kind of precedence.  But it's not in the formal rules, so I guess not.

But I noticed that no one has answered my 48÷2x question, and it's techinically the same thing.  All you're saying is 48÷2abc.  I would still find 2abc and divide it into 48.  I guess it's because there's no actual multiplication sign in the expression.  It seems like you'd simplify it first.

[Xanthul]

Re: the 0.999... snafu:

Asking whether or not 0.999... = 1 is the same as asking whether 1/∞ = 0.

1 - 0.999... = 0.000...1

Pretty sure you can't do that.

Of course you can, it just reduces the argument. The 0.000...1 either represents an infinitely small number or zero, which is exactly what we are trying to determine. People who argue that 0.999... is not equal to 1 imply that 0.000...1 is in fact a number of measurable substance greater than zero, while those who argue that 0.999... is equal to 1 imply that 0.000...1 is zero. I do not agree that a number approaching a number, even to the point of being infinitely similar, can ever be equal to the number.

0.000...1 is not a correct number in any notation. You can't put a "1" at the end of an INFINITE string of zeros. That's the whole reason 0.999... is equal to 1, because there is no number inbetween and no difference between them.

1 - 0.999... = 0.000... = 0

[Ħ]

Why is the wrong answer winning.

[rumborak]

Why do people still say there is a right answer?

rumborak

[Ħ]

multiplication and division are of equal rank

/thread

[73109]

P
E
M
D
A
S

2 is the right answer.

[Ħ]

P
E
M
D
A
S

2 is the right answer.

You are misinterpreting PEMDAS.

P
E
MD (in order of left to right)
AS (in order of left to right)

[MetalManiac666]

I love how people are choosing 2, and then giving PEMDAS as the reason.  It's PEMDAS that shows that 288 is the correct answer.  It's only when you take into account implied multiplication that the answer comes out as 2.

[Implode]

I love how people are choosing 2, and then giving PEMDAS as the reason.  It's PEMDAS that shows that 288 is the correct answer.  It's only when you take into account implied multiplication that the answer comes out as 2.

[The Degenerate]

P
E
M
D
A
S

2 is the right answer.

You are misinterpreting PEMDAS.

P
E
MD (in order of left to right)
AS (in order of left to right)

THIS. The only people saying 2 are those that mistakingly believe that multiplication takes priority over division in all equations, which is incorrect.

[kári]

Re: the 0.999... snafu:

Asking whether or not 0.999... = 1 is the same as asking whether 1/∞ = 0.

1 - 0.999... = 0.000...1

No. Please go learn some more math so you know what you are talking about.
Also, 1/∞ = 0. Not infinitesimal, not undefined, it's 0.

Why do people still say there is a right answer?

rumborak

Because there is... Regardless of whether you think it is bad syntax or not, the right answer is 288.

[jsem]

How long does this have to go on? Lol.

Move to P/R?

[ScioPath]

Re: the 0.999... snafu:

Asking whether or not 0.999... = 1 is the same as asking whether 1/∞ = 0.

1 - 0.999... = 0.000...1

No. Please go learn some more math so you know what you are talking about.
Also, 1/∞ = 0. Not infinitesimal, not undefined, it's 0

"Learn math or gtfo." brilliant constructive answer. Kari, I think you misunderstand that what I posted is entirely hypothetical. What people are implying when they say 1 is not equal to 0.999... is that there is an infinitessimal difference between it and 1. I just took the problem and rephrased it to better state the problem at hand. Why am I getting so much "derp, you can't do that," crap?

Also, I am a bit confused, are you saying the infinitesimal doesn't exist? If an infinitely large number exists, why doesn't an infinitely small number exist, and why can't they be multiplied to be 1?

[XJDenton]

The notation you used implied an infinite number of zeros with a one on the end, which is nonsensical, as an infinite sequence can not have an end number.

[kári]

Re: the 0.999... snafu:

Asking whether or not 0.999... = 1 is the same as asking whether 1/∞ = 0.

1 - 0.999... = 0.000...1

No. Please go learn some more math so you know what you are talking about.
Also, 1/∞ = 0. Not infinitesimal, not undefined, it's 0

"Learn math or gtfo." brilliant constructive answer. Kari, I think you misunderstand that what I posted is entirely hypothetical. What people are implying when they say 1 is not equal to 0.999... is that there is an infinitessimal difference between it and 1. I just took the problem and rephrased it to better state the problem at hand. Why am I getting so much "derp, you can't do that," crap?

Also, I am a bit confused, are you saying the infinitesimal doesn't exist? If an infinitely large number exists, why doesn't an infinitely small number exist, and why can't they be multiplied to be 1?

That wasn't what I was saying, I was trying to say that what you wrote is entirely incorrect. You're confusing the set of real numbers with some extension of it that includes infinitesimal numbers. But that was never the point. The point is that in the set of real numbers, 0.99.. = 1.

Also in the set of real numbers, 1/∞ = 0. Infinitesimal numbers "exist", but not in the set real numbers. ∞ is also not an element of the set of real numbers, that's why, when working with it, certain operations have been exactly defined. 1/∞ = 0 because lim(x->∞)(1/x) = 0.

Also, writing the infinitesimal difference between 1/∞ and 0 in that extended set of the reals as 0.00...1 makes no sense as well. There is no 1 at the end, since there is no end. There's no way to write an infinitesimal number like you would write another real number. Just like you can't write infinity, which is why the symbol ∞ was introduced. What you mean when you say that 1/∞ is infinitesimal is that 1/∞ is as close as you can get to 0, without writing 0. It has no meaning however.

[robwebster]

The notation you used implied an infinite number of zeros with a one on the end, which is nonsensical, as an infinite sequence can not have an end number.

That's the exact point of the debate, though, surely? Whether there's a difference between something that's infinitesimally small, and something that doesn't exist.

I'd say the difference between the two is nil, and I'd therefore say that nought point nine-with-a-dot-above-it is equal to 1. I agree with you.  But it's not a foregone conclusion, I don't think. I wouldn't tell anyone who disagrees with me to learn more maths. Poss to reconsider, but I get where ScioPath was coming from. The point of the ... isn't saying that the series ends, rather to demonstrate that the eventual "...01" is always, always a step further away.

[Orbert]

The only people saying 2 are those that mistakingly believe that multiplication takes priority over division in all equations, which is incorrect.

No.  There are some who were taught that implied multiplication pre-empts normal left-to-right precedence and have yet to hear any counterargument.  It is not the same issue as order of operations.

[kári]

The notation you used implied an infinite number of zeros with a one on the end, which is nonsensical, as an infinite sequence can not have an end number.

That's the exact point of the debate, though, surely? Whether there's a difference between something that's infinitesimally small, and something that doesn't exist.

I'd say the difference between the two is nil, and I'd therefore say that nought point nine-with-a-dot-above-it is equal to 1. I agree with you.  But it's not a foregone conclusion, I don't think. I wouldn't tell anyone who disagrees with me to learn more maths. Poss to reconsider, but I get where ScioPath was coming from. The point of the ... isn't saying that the series ends, rather to demonstrate that the eventual "...01" is always, always a step further away.

I wasn't trying to be rude or so, I was just trying to say that in order to really know what you are talking about you have to know some stuff about certain branches of math. If you don't, you don't really have much ground to stand on. This is not like the original topic of this thread where anyone can participate as the problem is mundane.

It would be like you or me joining some quantum physicists in a discussion about quantum entanglement and go "Hey, why are you debating this? It can't be possible for something to have an effect on something else without anything in between knowing about it". Or astrophysicists discussion black hole radiation and saying "Black holes can't emit stuff, nothing can escape them, not even light."

[Jamesman42]

No.  There are some who were taught that implied multiplication pre-empts normal left-to-right precedence and have yet to hear any counterargument.  It is not the same issue as order of operations.

^Turns out this may be true: https://mathforum.org/library/drmath/view/54341.html

Although the most common way is to do it the way to get 288, not 2. I still stick with 288, but I am more with rumby that it's just bad syntax, and I agree with the above article that parentheses are definitely a plus to make sure there is no ambiguity. Parentheses are an expression's best friend, and they can be yours, too.

I was taught left to right and not the implied multiplication (never heard of IM until this thread).

[kári]

Same here James. Either way, it's not a standard form, nor should it be. Parentheses should be used.

[Orbert]

(never heard of IM until this thread)

Me neither, at least not as a formalized term.

[lonestar]

Day 3, and the battle still rages.

[Orbert]

Awesome, isn't it?

[lonestar]

It's especially entertaining to me because I am worthless at math.  It would be like you guys watching me and ten other chefs arguing whether sous vide or slow roasting garners a better duck breast.

[jsem]

It's especially entertaining to me because I am worthless at math.  It would be like you guys watching me and ten other chefs arguing whether sous vide or slow roasting garners a better duck breast.

I don't even know what you're talking about...

[lonestar]

It's especially entertaining to me because I am worthless at math.  It would be like you guys watching me and ten other chefs arguing whether sous vide or slow roasting garners a better duck breast.

I don't even know what you're talking about...

My point exactly.

[Orbert]

Did someone say "breast"?

[Jamesman42]

Saying "breast" in a thread about math is like giving a 12-year-old boy a copy of Maxim after a dog has torn it up. Such a tease and that's all we are getting.

[XJDenton]

The notation you used implied an infinite number of zeros with a one on the end, which is nonsensical, as an infinite sequence can not have an end number.

That's the exact point of the debate, though, surely? Whether there's a difference between something that's infinitesimally small, and something that doesn't exist.

I'd say the difference between the two is nil, and I'd therefore say that nought point nine-with-a-dot-above-it is equal to 1. I agree with you.  But it's not a foregone conclusion, I don't think. I wouldn't tell anyone who disagrees with me to learn more maths. Poss to reconsider, but I get where ScioPath was coming from. The point of the ... isn't saying that the series ends, rather to demonstrate that the eventual "...01" is always, always a step further away.

As a conceptual argument that makes sense but he used the notion in a mathematical proof, which simply doesn't work.

[Ħ]

Implied multiplication is a lie.

Honestly, division signs and /'s are just amateur.  Real mathematicians use horizontal lines to indicate division.

[XJDenton]

Actually I think real mathematicians use whatever symbol their computer code uses, therefore allowing them to bugger off whilst it runs to drink some more coffee.