How to add two number in seconds ? Understand Mathematics

As a computer science student, i enjoyed mathematics pretty much. I started learning Machine Language and i started forgetting human language which you can see in my posts as well.

So Addition, what's special about it ?

Every operation a computer performs, is an addition for the system. It won't be incorrect if i say, computer can do nothing except Addition. So, a coder or a programmer design everything in form of operands and computers do addition over it directly or indirectly. We will discuss it in detail some other time.

Let's try to understand, the meaning of addition ?

1+1=2
2+2=4
3+3=6
4+4=8
5+5=10.. and so on.

What are we doing here ?
Yes, Doubling the integer with adding the same integer to it. Does this happen to negative integers as well ? Well No! Let's see

(-1)+(-1)=(-2)
(-2)+(-2)=(-4).. and so on.

Are they doubled ? Well, the answer is NO ! They are actually halved. This is a general doubt of doubling the negative integers. For example

(-2) is not double of (-1)
(-4) is not double of (-2).. and so on.

Actually the negative integers work in inverse manner, which means (-1) is double of (-2). Well, one can argue over this, but you can counter him with the basic definition of negative integers. (-2) is smaller than (-1), absolutely true. You got your answer.

Let's take another example

1+(-1)=0
2+(-2)=0
3+(-3)=0.. and so on.

What is happening here then ? Neither doubling, nor halving, so what exactly it is ?
Is it not an addition?
It definitely is.

Addition is an operand dependent operation, which can enlarge anything to infinity or can reduce something to minus infinity.

How to do addition in seconds ?

JUST PRACTICE