Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °
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#1 2010-03-20 22:45:06
#2 2010-03-20 23:00:19
- mathsyperson
- Moderator
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Re: Cute little problem I saw on another site
Ah, now I see how this works. Nice puzzle.
Why did the vector cross the road?
It wanted to be normal.
#3 2010-03-23 17:37:04
- scientia
- Full Member
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Re: Cute little problem I saw on another site
In general, for , we have
This can be proved by induction. For the inductive step, note that
Hence, for this problem,
#4 2010-05-07 05:54:09
- JaneFairfax
- Legendary Member
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Re: Cute little problem I saw on another site
scientia wrote:
In general, for , we have
This is a very neat formula. It also proves that if
then −1 ∊ Mn