Question

| a + b | < | a | + | b |. what is the proof of this? Thanks

Answer 1

let a and b be opposite signs

Answer 2

|3-5| < 3+5 right?

Answer 3

sorry its less than or equal to

Answer 4

Triangle inequality :D

Have you learnt dot product?

Answer 5

if same sign, we get equals

absolute value can be considered a distance between things.

opposite signs decrease distance, same signs increase distance

Answer 6

so how would a diagram for this look like?

Answer 7

amistre64 i dont think that that number proof is enough

Answer 8

its not proof, but it should lead to some ideas.

Answer 9

a and b are vectors