Question

a,b,x are Natural numbers.
a = b then a+x=b+x.
can this be proved in some way ?

Answer 1

begin with a = b

let x = 5

add 5 to both sides

a + 5 = b + 5

replace 5 with x

a + x = b + x

Answer 2

yes, if a = b, then obvioulsy the second equation is true. just plug in numbers like: 2=2; therefore, 2+x=2+x!

Answer 3

I would like a proof. Not an example

Answer 4

hint: proof by contradiction.

Answer 5

begin with a = b

let x = some natural number

add x to both sides

a + x = b + x

Answer 6

What are the axioms from which i can prove this ?