I don't know why I thought in this way , I ask : if a and b are real numbers and c is also a real number , now if a=b why a+c = b+c , and also why ac=bc , questions like this I don't know why I am asking , they seem to be stupid . What = means exactly . I know that numbers themselves are sets , and + can be considered as a function , from here I began to justify this and I justified it logically , question is : is there a formal way to justify this ???