reasons to believe, there is no God

[Tiberius]

To see the absurdity and contradictions of an actual infinite number of things in the real world imagine or hypothesize your campus library having an infinite number of black books and an infinite number of green books, alternating colours on the shelves and numbered consecutively on the spines.

Does it make any sense to say that there are as many black books as there are black plus green books together? But that is what you would have to say if you want to claim the infinite is possible in the real world.

Yes, it makes perfect sense in a mathematical model. See Hilbert's Hotel for more explanation.

Suppose you withdrew all the green books. How many books are there left in the library? There would still be an infinite number of books in the library even though we just withdrew an infinite number and found a way to get them home!

Yes, because you've already said there were an infinite amount of green books and red books. Nothing has gone against mathematics yet.

Suppose you withdrew the books numbered 4,5,6...and so on. Now how many books are left? THREE! Something surely is wrong here! One time we subtract an infinite number of books and we're left with an infinite number; the next time we subtract an infinite number and we're left with three - a clear logical contradiction.

It isn't a logical contradiction. You had two lots of infinitely many books. You removed all of one type, leaving you with infinitely many of the other type. You had two lots of infinitely many books again, but this time you removed all of one type, and all but three of the other type, leaving you with three. You are removing different amounts each time...of course you will get different results. Perhaps you should look up the concept of "countably infinite" things.

Since our hypothesis leads to a contradiction, the hypothesis must be false - a library with an actual infinite number of books cannot exist.

I don't think anyone was arguing the library could exist in reality, but it can still exist in mathematics perfectly fine. It doesn't exist in the real world because we don't have an infinite amount of space, not because there is something contradictory about infinity.

Therefore, since a beginningless past would be an actual infinite number of things (events) and since an actual infinite number of things cannot exist in the real world, it follows logically that the past is not infinite. The universe had a beginning.

Yes, the universe had a beginning, but this does not necessarily mean the universe hasn't always existed. It "began" in the sense that it "expanded" (Big Bang), but before the Big Bang, it is theorised that time did not exist, ergo there cannot be any cause and effect (because that requires time) and so the universe was a in a state of existence but with no time.