Model Boat Mayhem
Mess Deck: General Section => Chit-Chat => Topic started by: Neil on May 01, 2012, 01:36:10 pm
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Here it is........what is the penultimate real number (not an algebraic equation) to INFINITY %) %) %)
Don't ask me, I don't think that deeply, %%
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Well this is the big debate...
Anyone heard of Graham's Number? Not even Graham knows much about it but is in the Guiness world records for the largest proven number or something like that.
There was an interesting BBC horizon episode on infinity, certainly gave me a headache..
Dan
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Oh, an answer to the question i think would be infinity minus 1, which would equal infinity...
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There was an interesting BBC horizon episode on infinity, certainly gave me a headache..
Yes I saw that. Quite interesting!
Infinity + 1 = Infinity
Infinity - 1 = Infinity ?!?!?
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but those are algebraic equations, sorry!
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Chaps...have you all been on the wacky baccy?
I worry about you lot, I really do...
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Infinity - infinity = 0? :}
Well Neil, im afraid there is no answer.
Its been mathematically proven that 2+2 doesn't actually equal 4 and so how far can we actually trust maths? I had a discussion about something of this nature with a mathematician at the weekend and its really quite fascinating. Id love to do it at degree level.
Its like pi, it never ends but to how many decimal places should we work to? Where do we draw the line.....
I found the googolplex thing interesting also - that if each atom was placed (in the know universe) on each digit, there would be loads of spare digits left over.. Infinity is much much bigger than that and consists of numbers we havn't even found a name for, mainly because there is no need.
Its a very interesting subject which mathematicians need to be careful about when dealing with.
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but those are algebraic equations, sorry!
...??? ... OK I don't know what that really means. {:-{
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Infinity - infinity = 0? :}
Its been mathematically proven that 2+2 doesn't actually equal 4....
1 + 1= 2...1 + 1 = 2...2 +2 = 4. End of story.
Isn't it?
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1 + 1= 2...1 + 1 = 2...2 +2 = 4. End of story.
Isn't it?
Let A = 1.99999999...
10 X A = 19.999999...
Subtract A from each side...
10A - A = 18.0
9A = 18.0
A= 2
Therefore as A = A 2 = 1.99999 ... so perhaps not quite end of story.... {:-{
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:-))
Lol, you can do nothing but look at and think about this stuff and laugh. Its mind boggling, although very interesting.
Maybe someone will get to the bottom of this one day..
Dan
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As far as Pi is concerned, surely its to the nearest pencil thickness, 4H being more accurate than 2B?! or a crayon :}
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3/7d...
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Its been mathematically proven that 2+2 doesn't actually equal 4
When I was was young I learned that 2 + 2 = 4. How naive I must have been. Far to vague.
I then went to college and found that 2.00 + 2.00 = 4.00, a level of precision that with extra decimal places should cover every eventuality.
WRONG !
My wife is a Bookkeeper. Shes assures me that in Accountancy 4 is the one value it can never be. The answer is either 3 or 5, depending on whether you are calculating for the Tax Return or the Shareholders.
Anyway, this all sounds like an "Ultimate Question" for "Deep Thought", in which case the answer is of course 42 {-)
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Imagine a perfect circle Neil
You have just achieved something that neither nature nor maths can show you . I think that arguement
on perfect or 'ideal' shapes goes back to Plato. Now apply your 'ideal' to approaching infinity - so you already
imagine the answer but you can never demonstrate or verbalise it - though you can easily communicate it to
those willing to imagine. The paradox is that every responsive answer to your suggestion will be utterly unique.
If I am forced to be only logical then to give '1' a definite value I must first ask what is 1? a digit, a distance, an
infinity? I am defeated by the logic of others almost immediately.
I admit I also like Bob's '42' answer ......... a very nice age for a model %) {-)
Dave
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3/7d...
That was an expensive pi back in pre decimal days.
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http://youtu.be/2jGzadMkwb0 (http://youtu.be/2jGzadMkwb0)
http://youtu.be/oJS8GszWJuQ
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To add to the confusion:
There are an infinite number of integers.
There are also an infinite number of prime numbers, natural numbers greater than 1 that have no positive divisors other than 1 and itself
So, there are obviously fewer prime numbers that integers but both are infinite
They say mathematicians produce no new work after the age of 40 ..... I am not surprised !
Don't have sleepless nights !
Regards
Bob
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well, my flabber is gasted....if I'd have known earlier that i could have got all you lot working and thinking in such unison.........I'd have posted the question before.....
so as no one came up with the answer finite.....I'll post an easier one........
how is a hailstone formed.....and no looking on Wikky either.
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Rain rising to a colder layer of air forms hail.
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To add to the confusion:
Ah, but some of us have heard of aleph_0 and are wise to the countably infinite. %%
Andy
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I admit I also like Bob's '42' answer ......... a very nice age for a model %) {-)
Not sure about the age, but if her stats begin with 42, she's got me interested ;)
Mark.
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Let A = 1.99999999...
10 X A = 19.999999...
Subtract A from each side...
10A - A = 18.0
9A = 18.0
A= 2
Therefore as A = A 2 = 1.99999 ... so perhaps not quite end of story.... {:-{
Good try but it is the end of story.
That is using numbers incorrectly like the subtraction examples that leaves a residue instead of Zero result when all units are subtracted.
Hence why maths has set way to add, subtract, divide etc so 2+ 2 equals two, or is it 3 or 5????????????????
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how long is a piece of string? but it must be tied to a skyhook
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Neil,
This is like the questions i ask myself every day using CNC equipmnet ... they should be precise but there is a human elemnet ....
I will leave now my head hurts....
regards,
Kim
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how long is a piece of string?
Now we are into String Theory, which makes no sense at all except to mathematicians.
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Now we are into String Theory, which makes no sense at all except to mathematicians.
Next to come is what came first the chicken or the egg.
Thank you Neil mayhem abounds O0 O0 %% %% {-) {-)
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Here it is........what is the penultimate real number (not an algebraic equation) to INFINITY %) %) %)
Umm... Which infinity?
Before around 1870, mathematical discussions of this kind would be answered by explaining that infinity was not a number, but rather a conceptual limit which marked the end of certain kinds of mathematical process, such as series.
Then Cantor gave us the transfinite numbers, and upset a lot of apple carts. These are numbers which can be shown to be bigger than 'infinity' by using a principle called 'cardinality'. The concept is complex, and is best dealt with in set theory (which Cantor invented to describe it), but briefly, if there exists a simple 'pairing' between two sets of numbers, those number sets have the same cardinality. Cantor showed that that, for instance, the set of real numbers (R) and the powerset of the set of real numbers (P(R)) do not have this simple pairing, and hence P(R)>R under all circumstances, including when R is infinite. Cantor used the Hebrew term 'aleph' to depict a cardinality, and thus increasing sizes of infinities which are bigger than each other are described by the terms 'aleph-zero', 'aleph-one' ...etc
Useful mathematics can be done with these concepts. Cantor's set theory underlies all sorts of things, such as Turing's 'halting' work. Alas, the limitations of the standard set of characters on this board make it difficult to go further. The Wiki provides some useful introductions:
http://en.wikipedia.org/wiki/Cantor's_theorem (http://en.wikipedia.org/wiki/Cantor's_theorem)
http://en.wikipedia.org/wiki/Hilbert's_paradox_of_the_Grand_Hotel (http://en.wikipedia.org/wiki/Hilbert's_paradox_of_the_Grand_Hotel)
http://en.wikipedia.org/wiki/Cardinality (http://en.wikipedia.org/wiki/Cardinality)
http://en.wikipedia.org/wiki/Hyperreal_number (http://en.wikipedia.org/wiki/Hyperreal_number)
...
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Jeeze !!!!!!!!!!!!!!!!!!
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I'm astounded at how many deep thinkers we have on Mayhem :o About as deep as my thinking gets is what boat will I build next or... will I have a cup of tea or coffee %% {-)
Peter.
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I'm with you as I thought 2 + 2 model boats equaled four model boats but I can't see five yet can see three model boats.
Strewth am I confused %% %% %% %%
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Here's one for you
Why are chinese Amps smaller than the rest of the world?
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And another:
If infinity means going on for ever then it has no beginning and no end, therefore, if there is no beginning we arent really here. :D
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Next to come is what came first the chicken or the egg.
That's an easy one...... Fish and later on Amphibians were laying eggs long before birds evolved on the planet, so the Egg as a means of reproduction was established long before the advent of the Chicken.. :}
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I'm astounded at how many deep thinkers we have on Mayhem .....
Amongst other people, Galileo addressed the issue of adding and subtracting from infinity in his Two New Sciences (1638), and 'concluded that the ideas of less, equal, and greater apply to finite sets, but not to infinite sets.' That last phrase is directly lifted from a wiki entry - see http://en.wikipedia.org/wiki/Galileo's_paradox (http://en.wikipedia.org/wiki/Galileo's_paradox) for the reasoning behind that statement. So Galileo's answer would be that infinity-1 breaks the rules and does not really exist.
After Cantor, an alternative approach, and the one usually used by current mathematicians, is the use of transfinite arithmetic, as evidenced by Hilbert in his famous 'Hotel' illustration, where he uses Cantor's pairing argument to show that 'infinity+1=infinity' (at aleph-null cardinality). Similarly, infinity-1 would also equal infinity. And, before you ask, yes, there is an aleph-infinity cardinality. It's called aleph-aleph null ....
Have a look here: http://io9.com/5809689/a-brief-introduction-to-infinity (http://io9.com/5809689/a-brief-introduction-to-infinity) Nothing deep with this - it's just maths, which is a simple process of following the rules. Unlike some the problems in life that I do have difficulty with, such as why I cannot get the transom on my boats to stay at 90 deg to the keel, and why my wife complains if I use her shoes to hold a sheet of balsa down when gluing....
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I'm not a deep thinker, at least I can't remember if I am
But going back to the original question it's clear that its a trick(ish) question
because
infinity isn't a number, its a reference to a conceptual number, so in itself its a formula (for a given value of formula)
So if the brians of Mayhem are nicely warmed up:
What is red and invisible?
andrew
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Come on you Brians {-) {-)
Ned
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What is red and invisible?
andrew
A submerged Russian submarine?
Dave
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What is red and invisible?
andrew
Infra Dread, as opposed to Ultra Violent ?
[ another Douglas Adams quote, he has some interesting mathamatical concepts too ]
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3 men check into a hotel and the cost for the room is £30, they each pay £10 and go to their room.
After they have gone the man on the reception realises he has over charged and the room should be £25 not £30.
He takes 5 x £1 coins out of the till. realising he cannot split the refund 3 ways he decides to pocket £2 and give each of his guests £1 back.
So each man in the room has now paid £9.
3 x £9 is £27 and the £2 the receptionist pocketed = £29 , where has the other £1 gone?
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9 quid each = £27, LESS the £2 in the receptionists pocket = the £25 it should have been.
What is red and invisible?
a/ Stealth post office van.
b/ No tomatoes.
And for really deep thinkers - http://www.youtube.com/watch?v=6zkZ3f8DnKs
An old one, but well worth the visit.
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To add to the confusion:
I know that the square root of minus one utiises i the imaginary number
and that has allowed amazing technologies to arrive ....... but that does take
us right back to our capacity to imagine
I imagine I am late for work now <:( - gotta go >>>>>>>>>>>>>
Dave
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I don't have a problem with the square root of minus one - I met in, head on, in trying to understand quaternions. %%
Seeing it as a "y axis" to the real number "x axis" was good enough for my head. That it ultimately Doesn't Make Sense is neither here nor there. :-))
Andy
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That it ultimately Doesn't Make Sense is neither here nor there. :-))
Andy - that might be the most sensible thing said on Mayhem since the meltdown
A woman on a tv documentary said earlier '1 in 7 of men in the UK suffer with depression'
I think the rest of us simply enjoy it; being depressed is the best it's going to get anytime soon.
....... ah well, I'm just off to work now :((
Dave