Math problem that is driving the Internet crazy

[Haipule]

This is a simple duplication problem that non of you can see. 1 + 1 = 2, 2 + 2 = 4, 4 + 4 = 8 and 8 + 8 = 7, 16 + 16 = 32 (7 + 7 = 5) which is 5 and 5 + 5 = 1. So, the sequence 1,2,4,8,7,5 is infinite as long as there is no number higher than 9. I hate 10 because it is 1! What about 3,6,9? PLEASE tell me! Sorry, the answer to your question is 7--duh!

(bold mine)

I think I've spotted part of your problem.

Boru

There is no number higher than 9. So, 8 + 8 = 16 or, 1 + 6 = 7--DUH! Just like 16 + 16 = 32. Not so fast as 3 + 2 = 5 or, 7 + 7 = 14, 1 + 4 = 5 as there is no higher number than 9. Then 32 + 32 = 64. There is no number higher than nine so 6 + 4 = 10. There is no number higher than nine so, 1 + 0 = 1 and 64 + 64 = 128, 1 + 2 + 8 = 11 there is no higher number than nine so, 1 + 1 = 2. Get it? It's a fun toy to play with and it is infinite. 1,2,4,8,7,5,1,2,4,8,7,5 it never ends.

[Rev. Rye]

I think you need a base higher than 10 for that.

[Haipule]

I think you need a base higher than 10 for that.

Base 10 is for pussies! Much of what we live is base 60. 6 + 0 = 6. We can't get out of it! 60 seconds, 60 minutes! All times 10! Fuck 10!

Just being silly. Excuse my sense of humor. I meant no offence to you Rev. Just laugh at me like everyone else does. Really? Do they want me to explain my genius? Dream on!

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I can't even teach them light!

[GrandizerII]

This isn't a "maths problem". It's a "maths communication problem". And in this case, the communication spins on very shallow conventions.

There wouldn't be a big issue if we decided to change the convention tomorrow and say that division now takes priority over multiplication. Changing that convention doesn't change division. It doesn't change multiplication. It doesn't change arithmetic. It doesn't change the mathematics at all. This isn't a matter of mathematics.

Who cares about the conventions we use to denote the original calculation? We might as well be arguing over whether the Earth is 93 million miles from the sun or whether it's actually 150 million kilometers from the sun.

You can use whatever convention suits you, as long as you're consistent with that. But the point is that, if we're going strictly with the current PEMDAS/BODMAS rule ... not with some outdated convention that some people still use today and not with some future convention, but with the PEMDAS rule as it is ... then the parenthesis must be resolved first and then you divide and multiply from left to right. DIstributing the 2 in to the (2+2) before dividing violates that.

And this is after all grade/high school mathematics, so whatever convention engineers or physicists or advanced mathematicians use is not relevant here.

[A Toy Windmill]

This isn't a "maths problem". It's a "maths communication problem". And in this case, the communication spins on very shallow conventions.

There wouldn't be a big issue if we decided to change the convention tomorrow and say that division now takes priority over multiplication. Changing that convention doesn't change division. It doesn't change multiplication. It doesn't change arithmetic. It doesn't change the mathematics at all. This isn't a matter of mathematics.

Who cares about the conventions we use to denote the original calculation? We might as well be arguing over whether the Earth is 93 million miles from the sun or whether it's actually 150 million kilometers from the sun.

You can use whatever convention suits you, as long as you're consistent with that. But the point is that, if we're going strictly with the current PEMDAS/BODMAS rule ... not with some outdated convention that some people still use today and not with some future convention, but with the PEMDAS rule as it is ... then the parenthesis must be resolved first and then you divide and multiply from left to right. DIstributing the 2 in to the (2+2) before dividing violates that.

And this is after all grade/high school mathematics, so whatever convention engineers or physicists or advanced mathematicians use is not relevant here.

I think there is a more interesting point here, which is that there is a difference between mathematics and how we choose to express mathematics. It's one to keep in mind, since I think it diagnoses what so often goes wrong in the interminable 0.999... = 1 debate.

If we wanted to, we could write everything out in full:

Take 8 and divide it by 2. Multiple the resulting product by the result of adding 2 to itself.

This is the mathematics problem: finding out the value of a particular computation. It's an unwieldy way to set the problem (but there was a time when all problems were set in full prose), and nowadays, I take advantage of operators to write

(8/2)(2 + 2)

But I'm still expressing the exact same mathematical problem. The notation here depends on conventions, as does any notation or language in general. But once you understand the notation as popularly understood, you see it's the same problem I wrote above in full.

What is driving the internet crazy then is the fact that, it seems, many of them never really got to grips with some notation that's popular in high-school. This isn't an embarrassment for working mathematicians, because working mathematicians never use the division symbol. All our divisions are expressed using fractions, almost always with a horizontal bar so it's unambiguous where the numerator and denominator are.

We still insist that multiplication happens before addition, and I'd personally be sad to see the internet being confused over that convention, but it still wouldn't be too big a deal. I'd be happy to let majority vote determine which notational conventions we should use going forward.

But if the internet was being driven crazy by the problem expressed in full-prose, that would be a serious problem. I would not let a majority vote determine who was right in that case, and would be very worried about the state of our education systems.

[A Toy Windmill]

This is a simple duplication problem that non of you can see. 1 + 1 = 2, 2 + 2 = 4, 4 + 4 = 8 and 8 + 8 = 7, 16 + 16 = 32 (7 + 7 = 5) which is 5 and 5 + 5 = 1. So, the sequence 1,2,4,8,7,5 is infinite as long as there is no number higher than 9. I hate 10 because it is 1! What about 3,6,9? PLEASE tell me! Sorry, the answer to your question is 7--duh!

3 and 6 spin together forever, of course. 9 is stuck, because you don't get anywhere by doubling 9.

[polymath257]

OK, so the problem is 8/2(2+2).

Everyone agrees that the 2+2 is evaulated first because it is in the parentheses. So the question is the value of

8/2*4

This is an ambiguous expression. But that means we turn to convention. In this case, the *convention* is that multiplication and division are at the same level of precedence and we do the calculation from left to right.

Hence,

8/2*4=(8/2)*4=4*4=16.

Now, it is *possible* to have a convention where multiplication is done before division, which would give

8/2*4=8/(2*4)=8/8=1.

But this is NOT the convention actually adopted in mathematics.

Now, as a mathematician, I would *never* write an expression like this simply because it is ambiguous. I would put in parentheses to make it clear what is intended.

[GrandizerII]

OK, so the problem is 8/2(2+2).

Everyone agrees that the 2+2 is evaulated first because it is in the parentheses. So the question is the value of

8/2*4

This is an ambiguous expression. But that means we turn to convention. In this case, the *convention* is that multiplication and division are at the same level of precedence and we do the calculation from left to right.

Hence,

8/2*4=(8/2)*4=4*4=16.

Now, it is *possible* to have a convention where multiplication is done before division, which would give

8/2*4=8/(2*4)=8/8=1.

But this is NOT the convention actually adopted in mathematics.

Now, as a mathematician, I would *never* write an expression like this simply because it is ambiguous. I would put in parentheses to make it clear what is intended.

Thanks for that, polymath. Would it be accurate to say that the convention used to be the case that 2 would've been multiplied by (2+2) first, and then divide 8 by that result, but that it was later changed to the current one?

[BrianSoddingBoru4]

There is no number higher than 9.

Burn.

Boru

[polymath257]

OK, so the problem is 8/2(2+2).

Everyone agrees that the 2+2 is evaulated first because it is in the parentheses. So the question is the value of

8/2*4

This is an ambiguous expression. But that means we turn to convention. In this case, the *convention* is that multiplication and division are at the same level of precedence and we do the calculation from left to right.

Hence,

8/2*4=(8/2)*4=4*4=16.

Now, it is *possible* to have a convention where multiplication is done before division, which would give

8/2*4=8/(2*4)=8/8=1.

But this is NOT the convention actually adopted in mathematics.

Now, as a mathematician, I would *never* write an expression like this simply because it is ambiguous. I would put in parentheses to make it clear what is intended.

Thanks for that, polymath. Would it be accurate to say that the convention used to be the case that 2 would've been multiplied by (2+2) first, and then divide 8 by that result, but that it was later changed to the current one?

No. As far as I know, the convention has always been to go from left to right with multiplication and division at equal precedence. And, I might add, to not write such expressions (use parentheses) because they are likely to be misinterpreted.