Basic confusion in real analysis I have just started real analysis (first time) and self studying from book Mathematical analysis by Apostol.
In the first chapter of real and complex number system, it is written that

We assume there exist a non empty set R of objects ,called real numbers which satisfy the 10 axioms listed below .

1.But what is objects in this context ,is it number or could be a function or it could be anything ?
2.And if let's say it is given mathematical operation (addition) can be perform on the elements of sets,then objects must  be a number or function only?
 A: "Objects" is another word for thingamabob.
You have these thingamabobs that obey the axioms.  That's the only thing  you know about them.  They are thingamabobs that obey the axioms.

ut what is objects in this context ,is it number or could be a function or it could be anything ?

"nummm-burrs"?  "Funk-shun"? What are those words we have never hear of those words and don't know what they mean. (Actually maybe I have heard of "functions". If so these aren't "functions".  They are just things that exist in their own rights.)   This things are thingamabobs we just made up that obey those axioms.
But wait  "We assume there exist a non empty set $\mathbb R$ of thingamabobs ,called real numbers which satisfy the 10 axioms listed below ."
So these thingwhazzits are "numbers".  Every time we use the word "number" we will be talking these doohickies.
A: Part of the point is that you want numbers which have certain particular properties - but when you start it is not necessarily clear that the properties are all compatible with each other.
Taking an axiomatic approach (ie beginning with the properties), there are two questions to answer: "are there any objects at all which have this combination of properties?" (the existence question) and "do the objects which have this combination of properties behave like the objects I want to call 'real numbers'?" (the question of whether I have defined the right thing, and specified enough properties)
Once we answer those questions we can start calling the objects which have the properties 'real numbers'. It is a question of taking a step back and noticing the assumptions which are made when we call things 'real numbers'.
