While trying to prove that in real number system the sum of two continuous functions is continuous , I found a proof which is clearly understandable but I have encountered a property of real functions which I don't know how to prove.This one underlined with red.
If someone could help me with that I would really appreciate it . Thank you !
In mathematics, the qualifier pointwise is used to indicate that a certain property is defined by considering each value ${\displaystyle f(x)}$ of some function ${\displaystyle f.}$ An important class of pointwise concepts are the pointwise operations defined on functions by applying the operations to function values separately for each point in the domain of definition. Important relations can also be defined pointwise.
This definition of Pointwise operations from Wikipedia helped me to understand what was unclear to me , so I wanted to post it as an answer to my question.