The fascination of Maths thread

[moorfield]

Why does a Mobius Strip only have one side and one edge? Bizarre.

Why does my gran always say "Ooh, they're funny numbers." when hers are never drawn in the lottery? She'll never learn poor dear.

[BrilloPad]

I keep all the lottery numbers from the beginning - one day I am sure I will be able to use them to predict the winning numbers!

Obviously one has to predict numbers to maximize winnings - most popular choice is 123456!!! 10k pple per week do that!

[BrilloPad]

There was a physicist and an engineer working on a top secret time
travel project. Suddenly, there was a flash of light and there before
them was a very beautiful female life form.

She said to the men "I have been without companionship for many years,
if you can reach me, you can do with me as you wish" " However, because
of the time field, every time you move towards me you will go only half
that distance"

The engineer then looked at the physicist and noticed he was very sad.
"What's the matter with you, this is the opportunity of a lifetime !!"

The physicist replied "Don't you see, if I go only half the distance
each time, I will never actually get there ! It's a hopeless situation"
The physicist then asked the engineer "Why are you smiling ?"

The engineer grinned and said "That's true, ... but I'll be close enough
to get the job done !"

[VectraMan]

There are no uninteresting numbers:

Proof.

Suppose all the numbers up to 37 are considered interesting, but 38 is not. That very property (38 being the first dull number) could well be considered an interesting fact, and hence 38 is not dull after all. The same reasoning can be applied to 39 and so on.

Therefore, all numbers are interesting.

If you start from the premise that all numbers are dull, then there cannot be a first dull number as all numbers are dull. Therefore all numbers are uninteresting.

[Gonzo]

I keep all the lottery numbers from the beginning - one day I am sure I will be able to use them to predict the winning numbers!

Obviously one has to predict numbers to maximize winnings - most popular choice is 123456!!! 10k pple per week do that!

Those numbers are just as likely to win the jackpot as any other combination.

You'd be rather miffed if you had to share the jackpot with that many people though

[VectraMan]

Please follow the following arguments.
5/3=1.66
5/2=2.5
5/1=5
5/0.5=10
.....
....
5/0=infinity
and then 5/(-1)= -5
What you see? As the denominator is decreased the right hand side answer increases. The denominator becomes 3 then 2,then 1, then 0,then -1 ; and the answer increases, therefore -5 must be grater than infinity.
Where's the flaw. Please illustrate.

5/-0 = -infinity. But -0 and +0 are the same number, so 5/0 must be both +infinity and -infinity. And -5 is greater than -infinity, so all is well. Maybe.

Surely the reason is that the pattern follows the magnitude of the denominator and the answer, not the numerical values. It's the assumption that it's the numerical values at work that is the flaw.

[Denny]

There are no uninteresting numbers:

Proof.

Suppose all the numbers up to 37 are considered interesting, but 38 is not. That very property (38 being the first dull number) could well be considered an interesting fact, and hence 38 is not dull after all. The same reasoning can be applied to 39 and so on.

Therefore, all numbers are interesting.

Surely all or some numbers are neither interesting or uninteresting, depending on the opinion of the valuer and their knowlege of numbers and what they represent in relation to other numbers? The word 'interesting' is a value judgement not a fact, so there is nothing intrinsically remarkable or unremarkable about any number up to 37 or indeed beyond irrespective of what they represent mathematically.

Also, even if we were to accept that the number 38 was interesting, because it was the first dull number after 1-37 in the opionion of the valuer above, or for another reason. In relation to what? Just other numbers or in relation to something else?

If compared to, say, number 37, in the abstract, then it is probably no more or less interesting than 37 as I've already mentioned. But if the number 38 was the last number on your lotto ticket securing you the jackpot, even if number 37 was also one of the numbers you needed but not the bonus ball number, therefore rendering your ticket worthless up to that point, then the addition of 38 would be the most interesting number in the world, simply for what it signifies to secure you the big win. The same goes for 37, if that had been the bonus ball number instead.

The point I'm making overall is that intrinsic mathematical properties does not make a number interesting to everyone. So it's pointless stating it as fact. Also, whether a number is interesting can sometimes be based on non mathematical criteria.

[Diver]

Why does a Mobius Strip only have one side and one edge? Bizarre.

Why does my gran always say "Ooh, they're funny numbers." when hers are never drawn in the lottery? She'll never learn poor dear.

You will probably find this very interesting. I showed my Granddaughter these experiments with a Mobius strip, she is still fascinated.

http://www.metacafe.com/watch/331665..._mobius_strip/

[threaded]

I keep all the lottery numbers from the beginning - one day I am sure I will be able to use them to predict the winning numbers!

Obviously one has to predict numbers to maximize winnings - most popular choice is 123456!!! 10k pple per week do that!

Another amusing thing I notice at various clients with their lottery pools is the sets of numbers that are repeated on their tickets.

[NotAllThere]

Why does a Mobius Strip only have one side and one edge? Bizarre.

Ah. That's because a Möbius strip only has one side. Cos if you try to colour in just one side, you end up colouring both.

Apparently, there's an axiom you can add to ZF set theory called the Axiom of Choice. ZF theory is fundemental to nearly all mathematics. With the Axiom of Choice, you get ZFC set theory. The axiom of choice says that if you have a set A, which is a set of sets, then you can construct another set B, who's members comprise of one member of each of the sets within A.

This doesn't seem unreasonable.

However, it leads to, for example, a proof that there exists a series of translations and rotations that will transform five suitably defined sections of a unit sphere, into two unit spheres.

The thing is the axiom of choice tells you that you can construct a set, but it doesn't tell you how. Similarly the aforementioned proof tells you that you can do it, but doesn't tell you how.