Question

(- 1) + ? = – 2

1
-1
0
2​

Answer 1

Step-by-step explanation:

$x = - 2 + 1 = - 1$

Answer 2

Answer:

It follows easily from a very simple axiom of the real number system. You can take a look at those here.

Axioms are a bunch of ‘self-evident truths’ that one takes for granted, and then derives all results from them. Hence in Mathematics, when one asks for a ‘proof’ of something, one can go only as far as the axioms in general.

Take a look at axiom no. (P3) there. It says that, for every real number  a , there exists a unique number, denoted by  (−a), such that

a+(−a)=0−−−(1)  

Now, it follows that, for any number  (−a) , there exists a number  c  such that

(−a)+c=0.  

It follows that

c=−(−a).  

From equation (1) above, we get  c=a.  

Hence, we have:

−(−a)=a.−−−(2)  

Plug in the value  a=1  In equation (2) above, we get

−(−1)=1.  

Now, an alternative representation of  −(−1) is  (−1)×(−1).  

Hence, we have:

−(−1)=   (−1)×(−1)=(−1)2=1.  

QED.