Question

If 0 12 years ago

Answer 1

a<b and c>0 then ac < bc
ac < bd + bc -bd
ac < bd - b(d-c)
however, c<d , then d - c >0--> b(d-c) >0
so that bd -b (d-c) < bd
therefore ac < bd
Is there any mistake?

Answer 2

@phi

Answer 3

Is there any other way?

Answer 4

the logic looks ok to me.

There are probably other ways, but off-hand I don't know them.

Answer 5

Thank you. :)

Answer 6

how about
0<a<b
0 < ac < bc for c>0

0<c<d
0 < bc < bd for b >0

so
ac < bc and bc < bd
ac < bd

Answer 7

Yes, it is ok, also. :)