TITLE: Can I think of convergence as an independent mathematical object?
QUESTION [1 upvotes]: Recently I studied convergence of sequence of real numbers in an introductory analysis course. 

Can I think of convergence as an independent mathematical object just as we think of numbers and functions as mathematical objects?
If I can think of convergence as an independent object does there exist a larger class of objects to which convergence belongs, just like polynomials belong to the larger class of algebraic expressions?

REPLY [1 votes]: Convergence is more like a concept rather than an object. 
One can think about convergence of other objects. One cannot manipulate convergence as one usually does with mathematical objects.
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