Pretty simple ordered field question

[jaqueh]

Homework Statement

basically proving multiplying a negative number through an inequality changes the inequality

Homework Equations

if a > b, and c < 0,
then the following inequality holds: ac < bc.

The Attempt at a Solution

I am pretty stumped on this one, i tried to prove that C is a negative number, but i don't know where to go at all

 

[Hurkyl]

For the most part, it should be just unraveling definitions, and making use of the fact ad>bd for any positive d. (and picking a useful d)

 

[jaqueh]

i'm still stuck, all i can think of is making the d=-c which i define when c+(-c)=0

 

[jaqueh]

i'm still lost, i don't know why i am so bad at simple algebraic manipulations. can anyone offer more hints?

 

[Hurkyl]

i'm still stuck, all i can think of is making the d=-c which i define when c+(-c)=0

So make the substitution. How is < defined? Apply the definition both to this case, and to the case you're trying to solve, so that you can see what you need to prove.

 

[jaqueh]

I actually ended up figuring it out, thanks tho!

 

[Hurkyl]

I actually ended up figuring it out, thanks tho!

Ah good!