Which of these sockets are in the right place? (If any)

[JohnW2]

Yes .....
.... So people are asked "Which is greater, six dozen dozen or half a dozen dozen?"
They hear "dozen dozen" on both sides - so that's the same.
They hear "six" on one side and "half a dozen" on the other, so that's the same.
They don't realise that they've used one of the "dozen"s twice when they combine those and declare "six dozen dozen" and "half a dozen dozen" to be equal.
I can quite understand, when they hear the question once, and have to answer immediately, that some people get it wrong.

Ah, right. Thanks.
Again, I 'misinterpreted' the question. When ebee said that, although "6 dozen dozen" is clearly the greater, "many people get it wrong", I (probably subconsciously) thought that he meant that they said that "half a dozen dozen was greater"- and I still can't think of any sort of thinking that would result in that conclusion.
[ to be pedantic, the 'Yes' as he start of your message I have quoted above is therefore incorrect, since I had asked whether you could think of any way in which they could conclude that "half a dozen dozen" was the greater ]

However, as you point out, it's fairly easy to see why many (like Harry) might think that the two are the same (which is still 'wrong').

 

[EFLImpudence]

Has anyone pointed out?

"6 dozen dozen" is actually "half a dozen dozen dozen".

Now is it clear?

 

[ebee]

Stop being silly EFLI. I know you are doing it on put

 

[ebee]

One which used to drive my F-I-L mad was the 3 men in a hotel missing £1 question.

And one guaranteed to drive everyone mad was the Monty Hall gameshow one.

I reckon the F I L one is probably the same as the three fellahs and a second hand tv for sale as I heard it probably, yup a good in.

Indeed that Monty Hall did drive me mad, I gave up to it then weeks later when I was not thinking about it I suddenly whilst having a shave I twigged it. Simples. Viewing from a completely different angle sometimes solves things easy Peary. Strange world innit?

 

[EFLImpudence]

Stop being silly EFLI. I know you are doing it on put

No, my comment is correct and why some get it wrong.

 

[morqthana]

Has anyone pointed out?

"6 dozen dozen" is actually "half a dozen dozen dozen".

Now is it clear?

Which is greater, six gross or half a gross?

 

[morqthana]

[ to be pedantic, the 'Yes' as he start of your message I have quoted above is therefore incorrect, since I had asked whether you could think of any way in which they could conclude that "half a dozen dozen" was the greater ]

Yup - I didn't read your question carefully enough.

Oh, the irony.

 

[EFLImpudence]

Which is greater, six gross or half a gross?

What am I missing?

Presumably six of anything is greater than half of that thing.

 

[JohnW2]

And one guaranteed to drive everyone mad was the Monty Hall gameshow one.

Very much so, and we've discussed it here at some length in the past - but it still continues to intrigue me!

As I've reported before, on at least a couple of occasions I've been at international Statistics conferences at which very eminent statisticians have very nearly 'come to blows' over the answer.

It's rather different from what we've been discussing here, since the correct answer is so incredibly counter-intuitive, even to most of the world's greatest experts in the field of probability. In my case, I only eventually managed to convince myself that the correct answer was correct by undertaking computer simulations - but, to this day, (and like many Statisticians) still have difficulties getting my head comfortably around the theoretical 'explanation'!

The whole saga has caused quite a lot of concern amongst Statisticians and Mathematicians, since a high proportion of them would not have had any hesitation in saying that the correct answer was 'obvious' (even though incorrect) - hence making them now think more than twice before 'asserting' anhything!

 

[morqthana]

Quite a good explanation of the probabilities here: https://en.wikipedia.org/wiki/Monty_Hall_problem

 

[JohnW2]

Quite a good explanation of the probabilities here: https://en.wikipedia.org/wiki/Monty_Hall_problem

I've read dozens, if not hundreds, of explanations' in my time, as have many statisticians, but that doesn't alter the fact that most of us still have grave 'intuition problems'! There's also at least one PhD thesis about it knocking around!

As I wrote, the worry is that since what many experts regard as the 'obvious answer' is actually incorrect, they naturally worry about the correctness of other assertions they make about things which 'seem obvious' to them.

 

[opps]

So did I - but what you didn't seem to learn at uni was that "fraction" merely means "non-integer" and, as morqthana and myself have said, such a value can be expressed as either a "decimal fraction" or a "vulgar fraction" (sometimes called a 'simple fraction'), the latter being one integer 'over' another

I honestly don't recall hearing the the term decimal fraction either during my pure and applied A'level maths and definitely not whilst at univerversity. That said, both were a gazillion years ago. According to Google a decimal fraction is one where the denominator is a factor of 10.

So...

0.5 would be expressed as 5/10.

I was taught that a vulgar (improper) fraction was one where the nominator is larger than the denominator, eg 5/2.

Definitions on the web seem to vary, so I guess it depends on how old one is and where they were taught.

But hey, maths is not a perfect science, as is evidenced by paradoxes such as Gabriel's Horn. An infinitely large cone which, if filled with paint, would not contain enough paint to cover the outside of the cone. And don't get me started on imaginary numbers...

 

[ebee]

Good stuff, vulgar and improper will do me. Someone once pointed out that three out of two people do not understand fractions anyway

 

[JohnW2]

I honestly don't recall hearing the the term decimal fraction either during my pure and applied A'level maths and definitely not whilst at univerversity. That said, both were a gazillion years ago.

When I was at uni (also initially a gazillion years ago, although I've done some higher degrees more recently than that) it was very straightforward:

• "decimal" meant that a number is represented using the decimal number system - i.e. using digits 0-9 and with 'place values' within the number (both before and after any decimal point) differing by powers of 10.

•"fraction" simply meant non-integer, however represented.​

... hence 123.456 was a "decimal fraction', since it was non-integer and expressed in the decimal number system

According to Google a decimal fraction is one where the denominator is a factor of 10. So... 0.5 would be expressed as 5/10.

I'm not familiar with that use of the phrase, and it certainly did not have that meaning 'back then'. As above, it would probably not even have been regarded as decimal since, although numerator and denominator are both (I assume!) expressed in terms of the decimal system, the expression as a whole is not.

I was taught that a vulgar (improper) fraction was one where the nominator is larger than the denominator, eg 5/2.

In my day, that was called an "improper" fraction, "vulgar fraction" (or "simple fraction", or "common fraction") was any quantity expressed as a numerator divided by a denominator, using any number system for the two elements (I have vague recollections of having to play with "vulgar fractions" in which both numerator and denominator were octal, or maybe hexadecimal!)

Definitions on the web seem to vary, so I guess it depends on how old one is and where they were taught.

Agreed. My A-Levels and S-Levels (which included both Pure and Applied Maths) were best part of 60 years ago, and my initial uni education soon after that, but I also did some higher degrees in mathematical subjects some 25-30 years later - but all of that is 'pretty old'.

But hey, maths is not a perfect science, as is evidenced by paradoxes such as Gabriel's Horn. An infinitely large cone which, if filled with paint, would not contain enough paint to cover the outside of the cone.

Indeed, but one doesn't need to have had a very high level of mathematical education to have encountered that. The fact that a rotated curve could result in a cone of infinite surface area but finite volume was one of the early things we were exposed to when we started learning calculus for O-Level 'Additional Maths'.

And don't get me started on imaginary numbers...

Potentially mind-boggling, but extremely useful, even in electronics

 

[morqthana]

According to Google a decimal fraction is one where the denominator is a factor of 10.

If you just looked at the summary, rather than following link(s) to sensible looking sites, you were reading something produced by Artificial Intelligence Stupidity.