I don't understand why everyone in this thread is getting upset about the lack of axiom lists instead of actually googling axioms for real numbers and then getting on with the proof. Pretty sure there's only one list of axioms for real numbers.
ANYWAY.
The following proof is to show that the product of two negitive numbers equals a positive. I will assume a(-b)=0 but this can be deduced from the axioms anyway.
a+(-a)=0
(a+(-a))x-b= 0 x -b
=0
we know ax-b=-ab
-ab+(-ax-b)=0
so -ax-b=ab
I have gotten this far but am a little stuck with showing x^2>0
my attempt looks like this:
let x=-a
from the above we know -ax-a=axa=a^2
for the case x=a
axa=a^2
however this seems a little too simple to me.
If anyone could help constructively that would be great.
ANYWAY.
The following proof is to show that the product of two negitive numbers equals a positive. I will assume a(-b)=0 but this can be deduced from the axioms anyway.
a+(-a)=0
(a+(-a))x-b= 0 x -b
=0
we know ax-b=-ab
-ab+(-ax-b)=0
so -ax-b=ab
I have gotten this far but am a little stuck with showing x^2>0
my attempt looks like this:
let x=-a
from the above we know -ax-a=axa=a^2
for the case x=a
axa=a^2
however this seems a little too simple to me.
If anyone could help constructively that would be great.
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