Is there a finite amount of beings? According to the Buddhist teachings all beings are subject to Samsara and one can escape Samsara as he finds enlightenment.

But if all beings were ultimately to be reborn, with exception of those that reached enlightenment, wouldn't that mean that there is a finite number of beings, which only decrements?
Learning mathematics, I was warned to beware of logic based on an informal or naive definition of infinity (it is tricky and error-prone, see for example Zeno's paradoxes).

According to Wikipedia, 4th century BCE Jain mathematicians distinguished between "uncountable" and "infinite" (see ref and ref and ref) but I'm not sure that other (Buddhist) literature/authors supported a similar, specific, precise, or modern meaning of the word "infinity".

Some of The unanswered questions are questions about infinity: including whether the world is infinitely large, and whether it's eternal.

If these two questions were unanswered for good reason, then perhaps your question should be too.