## anonymous 3 years ago Use a proof by cases to show that min(a , min(b, c» = min(min(a , b) , c) whenever a, b, and c are real numbers.

1. anonymous

i guess you can grind it out with cases, for example if $$a\leq b\leq c$$ then $\min(a, (\min(b,c))=\min(a, b)=a$

2. anonymous

similarly if $$a\leq c\leq b$$ then $$\min(a,\min(b,c))=\min(a,c)=a$$ and so on

3. anonymous

4. anonymous

oh i guess you have to say for the first one that $$\min(a, \min(b,c))=a=\min(\min(a,b),c)$$

5. anonymous

likewise for the second. there may be a snappier way to do this, but it did say by cases, so just grind it out

6. anonymous

yw