Question

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.

Answer 1

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

Answer 2

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

Answer 3

thank you for clear answer

Answer 4

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

Answer 5

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

Answer 6

yw