Hi, I hope this is the correct forum, if not my apologies
I've been confused with this for a while and have decided I am really stuck.
I have to prove that |-a| = |a| using the absolute value definition which was given to us as:
Now I understand the following by definition:
if a>0 then
if a<0 then
But with I get really confused! My lecturer explained it as follows:
if , then,
and if , then
Firstly, Is this because originally we treat a as positive, but because it is made negative within the absolute value, then we treat it as if it is negative, thus -(-a)?
Then with a < 0, is it so because, we originally treat it as a<0, thus -(-a) but then as a negative, thus -a? Also with the RHS, -(-a) then -a?
Some clarification on this would be really appreciated, here is my attempt at proving it:
if , then
if , then
As you can see, I'm missing some small fact to make this true or I am making a really silly mistake somewhere as this seems like it should be very easy!