Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

You are not logged in.

## #26 2006-09-16 10:53:27

Dross
Member
Registered: 2006-08-24
Posts: 325

### Re: Battleship on the number line

mathsyperson wrote:

But surely...

Ricky wrote:

Now, let's make things interesting:

Would such a solution work on the rational line?  What about the real line?

Bonus points if you name the property of these numbers which gives the solution.

Indeed well spotted

Offline

## #27 2006-09-16 11:42:27

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

### Re: Battleship on the number line

Edit:

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

Offline

## #28 2006-09-17 05:55:43

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: Battleship on the number line

Ah, so by going at a speed of π mph it can evade our bombs forever. Pesky battleship.

Why did the vector cross the road?
It wanted to be normal.

Offline

## #29 2006-09-17 12:53:01

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

### Re: Battleship on the number line

Not exactly, mathsyperson.  It's not the fact that a number can't be wrote as a/b which makes it impossible to tell.  It's the number of numbers that can't be written as a/b which does.

Does that make sense?  In a sense, irrational numbers have a "higher infinity" than rationals.  There are more of them, in a sense, even though there are both an infinite amount of rationals and irrationals.

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

Offline

## #30 2006-09-17 13:17:36

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: Battleship on the number line

Yes, I get you.

Edit: That should probably be hidden or something.

Why did the vector cross the road?
It wanted to be normal.

Offline