Thread: Absolute values / summation proof

hi there,

I have trouble getting started with proving that:

abs ( sum over all a ) <= sum over all abs ( a )

any suggestions (induction proof) would be very welcome.

thank you -
oz.

Originally Posted by ozfingwe

hi there,

I have trouble getting started with proving that:

abs ( sum over all a ) <= sum over all abs ( a )

any suggestions (induction proof) would be very welcome.

thank you -
oz.

Exactly: induction (provided "over all a" means "over all the possible finite values some variable/parameter a can attain").

Tonio

Originally Posted by ozfingwe

hi there,

I have trouble getting started with proving that:

abs ( sum over all a ) <= sum over all abs ( a )

any suggestions (induction proof) would be very welcome.

thank you -
oz.

This is just the triangle inequality.