Question: I'm writing/starting with my bachelor thesis, the subject is about "infinity": what it is, why do we accept it, etc., but most of all my goal is to give an overview of the history of the interpretation from mathematicians (or maybe philosophic intellectuals).

So my concrete question is: I am looking for great 'history of mathematics' books, where the books focus on 'infinity' (ancient Greeks, etc.), so that I can show how the interpretation has changed through the past millenia, and why it changed. And what about the concept of infinity now? There are today still math professors who do not want to accept infinity.

Does anybody have good resources for the 'historical view of infinity'? Later, if I have time, I will extend it with some philosophical side tracks, but first I need the basis to fully understand, mathematically, what the concept is, how it developed etc.

Answer: 
The way I would go about this would be to take references from decent online papers and journals on the subject, and then research which of those might seem worth your money. I would pay particular attention to books about [Georg Cantor](https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=georg%20cantor).

Here is an example of such a book chase. A paper titled [A History of Infinity](http://www.math.tamu.edu/~dallen/history/infinity.pdf) was written at Texas A&M by a professor in the math department ([Dr. Allen](http://www.math.tamu.edu/~dallen/)). In the references to that paper, I see at least two stand out book sources:

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> Dauben, Josheph Warren, Georg Cantor, His Mathematics and Philosophy of the Infinite, Princeton University Press, Princeton, New Jersey, 1979
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and

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> Lavine, Shaughan, Understanding the Infinite, Harvard University Press, Cambridge, MA, 1994.
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If possible see if you can't survey 20 such references in this manner, secure from your library, possibly through inter library loan, and buy the ones you like the best after making your mind up as to whether the book is something you should own.

You will know when it is time to stop surveying and start picking acquisitions. Now you are ahead by at least two sources, but you might want to look at Dr. Allen's other references in that paper above as that looks like a pretty decent paper. You can certainly cite that online paper as well, it being from a reputable mathematician with the stamp of a university on it.
For the distinction of potential and actual infinity see [Transfinity](https://www.hs-augsburg.de/~mueckenh/Transfinity/Transfinity/pdf), in particular chapter I, but also a lot of sources in chapter V, and for some statements without references but easily to be found in the internet and pointing to further sources: the lecture slides <https://www.hs-augsburg.de/homes/mueckenh/HI/HI11.PPT> and <https://www.hs-augsburg.de/homes/mueckenh/HI/HI12.PPT>