What is wrong with this "proof" that all horses are the same color?

Let P(n) be the proposition that all the horses in a set of n horses are the same color.

Basis Step: Clearly, P(l) is true.

Inductive Step: Assume that P(k) is true, so that all the horses in any set of k horses are the same color. Consider any k + 1 horses; number these as horses 1,2,3,…,k,k + 1. Now the first k of these horses all must have the same color, and the last k of these must also have the same color. Because the set of the first k horses and the set of the last k horses overlap, all k + 1 must be the same color. This shows that P(k + 1) is true and finishes the proof by induction.

Designers Costume Designers Lighting, Tuning and Sound Designers also Sometimes same person will do two or more of those tasks Artists in professional world Costume Design: Clothing Gives us lots of information: time period, region, tradition, status, occupation, personality Professionals know what clothing to wear for different time periods and social status Designer Collaborative artist Strong art creative background Most studied theatre in college then furthered studies Help establish style of production Indicates period Considers line, color, fabric Helping tell story on stage Consider what character does; jumping around, flexible Scenic designer and Set designer