Any maths teachers on this forum?

I should probably have started reading on page 1 rather than at the last question set!

Who said they are free to choose their numbers and what's more why can't they produce an incorrect answer?

whooops ! a little "typo" I guess ?

In this crazy Universe we live in there are very few things that have a zero probability! (If any)

Oops. I was doing it from memory. Yes, 4100.

I've read the whole thread. This is the question in which people were asked to add 8 numbers together. I was talking about this question, where a number of people seem to erroneously get 5000 rather than the correct 4100 (not 4090 as I mistakenly said in a prior post). People who get 5000 are getting the same incorrect answer to the question, are they not? 

I think it is you who have the wrong question in mind. you should perhaps read the whole thread too ..

Well I thought as they were asked it was unrestricted, as in "Pick a number Bill", you pick twenty-seven and I say, no problem, pick another" but it doesn't matter. The real question is "Where's me coat?"

Check Please!

.......ever tried striking a safety match on a bar of wet soap.............? probability of success is zero.

and this is as certain today as it was yesterday, before I read our Brian's book "The Quantum Universe - everything that can happen does happen" - even our Brian accepts that in reality, somethings are a dead cert.

That is the source of my dismay with that lecturer.  When you represent a sequence with numbers  followed by 3 dots it means "The sequence is infinite and subsequent elements can be determined based on the obvious pattern."  In that guys world, the answer could have been "any number that != n-1" or "any integer > 0".  I don't know why I am nit picking this so much...  I guess I'm just getting flashbacks from the trauma that was Real Analysis. 

Kevin, no need to get upset, None of us did, and most of us opted for 64! - and those that didn't had simply got their sums wrong !!

He was making a very valid point about life in general. It stopped me "assuming" that life, people and descision-making etc could always be managed by mathematics, science, engineering or any other form of logical "order".

Seems you've just summarised The Second Law of Sociology, Don:

Some do, and some don't.

Chris

Freezing the soap may do it.  Even without this can you prove that it will never strike?  I mean really prove not just say it's obvious it won't.  What if it spontaneously combusts?  What if it is happening in a different atmosphere?

Prof Cox may have said that everything that can happen does happen but this is just something to please the punters.  Please quantify what is this "everything that can happen" and if it has happened then there is no future because it has already happened.  Again please proffer proof.

Over the years physicists have come up with some whacky ideas, like Everett's infinite dimension's idea or Richard Feyman's assertion that there is in fact only one electron in the whole Universe.  A lot of this is playing to the gallery.

To say "The Quantum Universe - everything that can happen does happen" is a meaningless statement, it's a kind of Zen for scientists.  It would be equally true to say "The Quantum Universe - everything that can happen will never happen".  If you disagree then please try to describe Prof. Cox's statement in real terms we can quantify.

I'm afraid you'll have to read the book yourself ! The ideas therein are Brian's way of explaining difficult concepts which in turn attempt to explain why things happen, that we might otherwise find surprising.

Of course, Brian makes it clear that Quantum theory doesen't enable us to predict everything  and one day, we will hopefully establish a theory that is a lot better..

So, the probability of striking a safety match on a bar of wet soap is so highly improbable, that in reality it is zero. Similar in concept to the idea that putting a kettle of water on a gas burner will cause it to freeze.

I summarised the

for the avoidance of doubt..........

.....when I say "Brian makes it clear......and one day we will hopefully establish a theory...."

...........I am not implying that myself and Brian work closely together on quantum theory....

Just think of a probability distribution over an infinite timespan.

"The Quantum Universe - everything that can happen does happen"

As I said is a meaningless statement firstly because Quantum Mechanics does NOT describe the whole Universe - Lookup the Theory of Everything.  Secondly as I asked earlier - what is everything that can happen?

Kevin if we think of probability distribution over an infinite timespan surely that would indicate that no event has a zero chance of happening.  Shame though, that as far as we know the Universe does not (and has not) an infinite timespan.  So I won't use that one.

The thing is: the Universe is an 'Uncertain' beast, that is what Heisenberg told us.  Now he may have been rubbish at getting the Nazi bomb working but he definitely was on form the day he elucidated the 'Uncertainty Principle'.  So please tell me how in an uncertain Universe we can have probabilities of 0 or 1?

With the soap thing there is a huge difference between " so highly improbable" and "in reality it is zero", that you simply cannot say that.  When does a very small number become zero?  If you take a number and keep removing 1% of its value are you saying that eventually it will become zero?  Surely you cannot believe that.  It will approach zero (or in maths we say 'tends to') but will never become zero.

In fact there is a very good case for saying that the number zero like the number infinity doesn't really exist, it is a figment of our imagination, or a mathematical necessity if you like.  It's a shame though, because if I have four apples and give 4 people one each then how many do I have left?  Well in integer math I have zero - but do the integers really exist?  In reality I will still have traces of apple on my hands etc.  It's like asking the question what is the average number of legs of Norwegian men?  The answer is something like 1.99 - it was actually done for Norway (or maybe somewhere else in Northern Europe).  But what is exactly one leg or 1.99 legs come to that?

I am rapidly becoming extremely boring, so before I bore everyone to death I will sign off.  Trouble is I am so sad that I find this stuff interesting.

Well not everything has to happen in this Universe.  I believe a part of the theory relies on the Multiverse.

Zero is a number and can be easily proved and integers do exist in nature. [If I have a solar system with 1 star and I give it to my friends solar system how many stars does my solar system now have?]

Oh dear!  What is a star, how can there be 2 stars.  It is what we understand in our view of the Universe that makes a star a star and not a ball of fusing atoms.  Each star is different.  So the concept of 1 star can only occur in our heads.  This is the crux of 'integers don't exist' argument and I must say that I do find it difficult to agree with it, even though I am arguing that cause.  Really all we are talking about is the way we look at things and in our minds we look at things very loosely.  Can you not see that your friend only has the concept of having 2 stars there are not 2 identical stars in the Universe, so he probably does not have 2 stars.  What he has is two of the things we call stars, ie it is a construct of our minds not the Universe.

I would very much like to see you prove that 0 does exist in a mathematically consistent and rigorous fashion.  But before you do have a look at Russel's proof that 1 + 1 = 2, it's a foolscap page of very dense set theory.  So brush up your set theory.

Greater minds that yours or mine have cast doubt on the existence integers and zero especially.  The existence of integers depends on their being identical things to count.  In fact in maths the only real use of integers is for indexing in series and other sets etc.

Arguably all applied mathematics is an imprecise model of reality. 

The "integers don't exist in reality" subset is simply simplest example of this concept to understand. We currently would argue that due to the inherent uncertainty at the quantum level, no two things could ever be identical. A model to replace quantum mechanics may come along, but it isn't likely that it will change the view of inherent uncertainty.

Pure mathematics doesn't even pretend to be a model of reality, but is only a construct of our minds, so doesn't negate the argument.

You would believe a bank manager?

The theory of everything won't replace Quantum Mechanics but will unite (we hope) Relativity and Quantum Mechanics, that is the current Holy Grail.

One of the most amazing facts about modern physics is that towards the end of the 19th century talented youngsters were being advised against a career in Physics because basically it was nearly all done and dusted, just a few little niggles to sort.

One of these little niggles was that the planet Mercury quite often was not where Newtonian mechanics said it should be.  The other little niggle was that the radiation from a black box couldn't be fitted to the classical theory.  The reason for the worry here was that the Classical Theory predicted that the energy of radiation would be way too high when we increase the temperature of the radiating body such that it was shifted to the UV.  In fact the theory predicted that it would have infinite energy by the time it reached the UV - a bit of a worry then.

From these two things sprang Special/General Relativity and Quantum Mechanics.  Good job that blokes like Einstein and Planck ignored the advice.

You could chop his head off and see if that makes a difference, it has been tried on Kings and Politicians and has been shown to work pretty well.  But not for Estate Agents, they carry on charging much too much for the little they do without or without a head.

If 0 does not exist then

x-x = y -->

x+(x-x) = x + y -->

x = x + y and x - y = x -->

x(x-y) = (x+y)(x-y) -->

x^2 - xy = x^2 - y^2 -->

y^2 = xy ->

y = x  ->

x = x +x ->

x = 2x ->

1= 2 an impossibility as Russel proved

Huh ! Looks like you find Relativity and Quantum Mechanics useful after all. Perhaps its just the way our Brian explains things, that you didn't like.

Most of us are probably pragmatic enough to go along with Euclid, Newton and a few others, even though there theories are often approximations when it comes to predicting the future outcome of our actions. How many times have "we" integrated "from zero to infinity" to solve some trivial problem and thus make life more comfortable. Or simply asked the shopkeeper for five apples and with French Golden Delicious, got 5 identical () but rather tasteless objects................