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

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## #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

Bad speling makes me [sic]

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## #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..."

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## #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.

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## #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..."

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## #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.

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