A Can infinity be observed in the real world?

[nnope]

To what extent is the term infinity used in the physical world.
When talking in terms of mathematics we can have a set of all natural numbers called an infinity, then we can have a value that comes after this set of infinity (lets call it 'a'). After 'a' comes 'a+1' then after this set of infinity comes 'B' and we can just keep making larger and larger sets of set of infinity. But is this real, can an infinity even actually be observed in the real world

 

[ObjectivelyRational]

If what you observe only consists of properties, attributes, things, or numbers of things having definite quantity, then you cannot observe infinity because it is "larger" than any quantity.

As an abstraction used in mathematics, the concept infinity, as used say in an infinite series or to describe certain limits, can be useful to calculate or characterize a finite quantity or behavior observed in reality, but a distinction should be made between the use of the abstraction and the observed quantity, one is math the other is reality.

If you can come up with a concrete example of something in the physical world which requires the concept "infinity" to describe it perhaps we can start the discussion there.

 

[pixel]

To what extent is the term infinity used in the physical world.

It is an approximation when anything larger will not make a difference at the precision level of interest. For instance, if we image a star with a lens, we can take the star to be an infinite distance away and the image at the focal plane of the lens. This should work for any star - there's no point distinguishing one star at 30 light years distance from another at 100 light years away. They're both "at infinity" so in the simple lens equation the 1/(object distance) term can be neglected.

For another example, see my post #4 in this thread: https://www.physicsforums.com/threads/electric-field-due-to-a-charged-sheet.868788/#post-5454334