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

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## #26 2006-09-17 08:53:27

Dross
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### Re: Battleship on the number line

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

## #27 2006-09-17 09:42:27

Ricky
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### 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..."

## #28 2006-09-18 03:55:43

mathsyperson
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### 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.

## #29 2006-09-18 10:53:01

Ricky
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### 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..."

## #30 2006-09-18 11:17:36

mathsyperson
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### 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.