A bit more Googling suggests that the concept of juxtaposition having a higher priority than a multiplication sign is far from being universally accepted.
A bit more Googling suggest that the concept of juxtaposition having a higher priority than a multiplication sign is far from being universally accepted.
I find it interesting that I do not think the juxtaposition should take precedence, but that my subconscious calculation of what was in front of me said otherwise.
Well I'm no mathematician, unlike others on the thread but for the number to be less than one, the amount it's less by has to be quantifiable and if the 9 is infinite then the difference between the 0.99999999999999999...... and 1 is incalculable.
Now someone who knows what they're talking about might explain it properly
Actually that does make sense. Maybe thats what the wikipedia page was saying but my denseness to maths rendered the whole thing incomprehensible!
No. In maths expressions the "context" is irrelevant. The symbols and the rules of computation are unambiguous.
If encountering such a thing in real life, the proper response is one (or all) of:
a) you're fired
b) WTF is this meant to mean
c) 0/10
though I would still (in the absence of clarification) take '2' as the answer.
Without context the expression in the OP is one of frustration, not mathematics.
Actually that does make sense. Maybe thats what the wikipedia page was saying but my denseness to maths rendered the whole thing incomprehensible!
Another way to look at it...
2 - 0.99999............ = 1.0000000000...........
Is 1.00000......... = 1?
The difference between 1 and 1.000000.... is the same as the difference between 0.999999...... and 1, but the human mind has an easier time rationalising 1.0000000.......
A bit more Googling suggests that the concept of juxtaposition having a higher priority than a multiplication sign is far from being universally accepted.
Just accept you were wrong mate
Was a fun discussion though... not many got it right.
So, if you use juxtapostion rules as stated above the answer is 2, but if you generally work left to right (after brackets) the answer is 288?
That's what it all hinges on.
It would seem that hardly any maths teachers, lecturers or text books mention juxtaposition so it looks like it's a huge way from being universally accepted.
The difference between 1 and 1.000000.... is the same as the difference between 0.999999...... and 1, but the human mind has an easier time rationalising 1.0000000.......
Yeah, I can see that. Thanks for somewhat renewing my faith in maths.
Well I'm no mathematician, unlike others on the thread but for the number to be less than one, the amount it's less by has to be quantifiable and if the 9 is infinite then the difference between the 0.99999999999999999...... and 1 is incalculable.
Now someone who knows what they're talking about might explain it properly
Having failed to start a ruck between Pure Mathematicians and the Applied sort, I'll be nice and say you may have missed your calling as that is more or less it
As you tend to infinity with your number of 9s (1 - 0.999999999) tends to 0. For every wee totty number "wtn" you can think of there is a number n such that (1- 0.99999999 repeated n times ) is less than wtn
It would seem that hardly any maths teachers, lecturers or text books mention juxtaposition so it looks like it's a huge way from being universally accepted.
It is a strange one.
My mathematics brain is saying that juxtaposition takes precedence.
My comp-sci brain is saying "bollocks".
The rest of my head is left wondering why these two haven't ripped each other to pieces over this issue in the last 37 years.
I believe, however, the latter should be expressed as such if it was intended to avoid ambiguity: 48/(2(9+3)).
Without the clarifying brackets it would make most sense in my mind to interpret it in the first way. That's obviously not the consensus among everyone.
In conclusion, no serious mathematician would touch a problem like this without additional clarity. The way it was written in the original post is intended to be ambiguous and cause exactly these type of arguments. If you passionately believe one side or the other, and brand others as "wrong," then you're just failing to accept the question itself is flawed and letting your ego cloud your ability to rationally see how both evaluations could theoretically be "right" as it stands. It's time to accept the question itself is the problem here.
It would seem that hardly any maths teachers, lecturers or text books mention juxtaposition so it looks like it's a huge way from being universally accepted.
It's the simple fact that 2 * (x + y) is not the same as 2 (x + y) in an expression/equation.
In conclusion, no serious mathematician would touch a problem like this without additional clarity. The way it was written in the original post is intended to be ambiguous and cause exactly these type of arguments. If you passionately believe one side or the other, and brand others as "wrong," then you're just failing to accept the question itself is flawed and letting your ego cloud your ability to rationally see how both evaluations could theoretically be "right" as it stands. It's time to accept the question itself is the problem here.
I was just about to post that the only conclusion I can draw so far is that the problem is ambiguous and can be interpreted either way, and no one has come up with any cast iron rule that proves it one way or the other.
It's time to accept the question itself is the problem here.
That is very true, but it raises some doubt about whether seemingly totally valid expressions such as a/bc should be evaluated as (a/b)*c or as a/(b*c).
Comments
I find it interesting that I do not think the juxtaposition should take precedence, but that my subconscious calculation of what was in front of me said otherwise.
Actually that does make sense. Maybe thats what the wikipedia page was saying but my denseness to maths rendered the whole thing incomprehensible!
In other words, either answer is technically correct.
Not really - 2 is the only correct answer because the juxtaposition rule applies.
If it was 2 x (3+9) then it would be 288 and only 288.
Bizarre.
a) you're fired
b) WTF is this meant to mean
c) 0/10
though I would still (in the absence of clarification) take '2' as the answer.
Without context the expression in the OP is one of frustration, not mathematics.
Another way to look at it...
2 - 0.99999............ = 1.0000000000...........
Is 1.00000......... = 1?
The difference between 1 and 1.000000.... is the same as the difference between 0.999999...... and 1, but the human mind has an easier time rationalising 1.0000000.......
Just accept you were wrong mate
Was a fun discussion though... not many got it right.
It would seem that hardly any maths teachers, lecturers or text books mention juxtaposition so it looks like it's a huge way from being universally accepted.
That is the problem. People are assuming that 2(3+9) is the same as 2 times (3 + 9) in any equation. It is not and has never been.
Yeah, I can see that. Thanks for somewhat renewing my faith in maths.
Having failed to start a ruck between Pure Mathematicians and the Applied sort, I'll be nice and say you may have missed your calling as that is more or less it
As you tend to infinity with your number of 9s (1 - 0.999999999) tends to 0. For every wee totty number "wtn" you can think of there is a number n such that (1- 0.99999999 repeated n times ) is less than wtn
It is a strange one.
My mathematics brain is saying that juxtaposition takes precedence.
My comp-sci brain is saying "bollocks".
The rest of my head is left wondering why these two haven't ripped each other to pieces over this issue in the last 37 years.
48
--- (9+3)
2
= 288
However, it could also be interpreted in this manner:
48
----
2(9+3)
= 2
I believe, however, the latter should be expressed as such if it was intended to avoid ambiguity: 48/(2(9+3)).
Without the clarifying brackets it would make most sense in my mind to interpret it in the first way. That's obviously not the consensus among everyone.
In conclusion, no serious mathematician would touch a problem like this without additional clarity. The way it was written in the original post is intended to be ambiguous and cause exactly these type of arguments. If you passionately believe one side or the other, and brand others as "wrong," then you're just failing to accept the question itself is flawed and letting your ego cloud your ability to rationally see how both evaluations could theoretically be "right" as it stands. It's time to accept the question itself is the problem here.
Cheers.
I was just about to post that the only conclusion I can draw so far is that the problem is ambiguous and can be interpreted either way, and no one has come up with any cast iron rule that proves it one way or the other.
So I agree with you.
"juxtaposition indicates multiplication of variables"
Therefore 2(12) should be replaced with 24...
Because your Mathematics brain knows that it has an unfair advantage and hasn't pressed it