Start with the following simple equation:
a=b
Multiply both sides by b:
ab=b^2
Subtract a^2 from both sides and factorize:
ab−a^2=b^2−a^2
a(b−a)=(b+a)(b−a)
Simplify and add 1 to both sides:
a=b+a
a+1=b+a+1
Now, since a=b (the starting point of this proof), we can write this as:
a+1=2a+1
And in the case where a=1, we have:
1+1=2+1
So, therefore,
1+1=3