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If we have an infinite amount of something and reduce it by 1 (or by a fraction of 1%) every time period for a finite number of time periods, could this amount then be reduced to zero?

Real physics example: If the universe beyond the Hubble Horizon is flat and infinite and has an ergodic, or statistically homogenous, distribution of matter throughout, which may very well be the case according to current cosmology, then the number of stars should be infinite. But stars cool, they burn up all their fuel and stop fusing. It will take trillions of years, but one day the last red dwarf in the universe will die as a black dwarf.

Is there a contradiction between cosmological and mathematical infinity?

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    "If we have an infinite amount N"... that's not a well defined concept. – 2017-01-06
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    Your underlying question is cosmological, not mathematical. Though I'm not a cosmologist, two serious flaws in the question's hypotheses appear to be 1. One's ability ever to see distant parts of the universe. (It's not true that "any two points of space are eventually causally connected.") 2. The concept of universal time implicit in "one day the last red dwarf [will burn out]." (There's no way to assign comparable notions of time for spacelike-separated events.) Contrary to Kronecker's famous quote, even the natural numbers are not faithfully modeled in the natural world. – 2017-01-06

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I guess there is no contradiction :

Assuming that every star has a bounded lifetime, and assuming that there is no new stars, it doesn't matters that there are infinitly stars. They will all die one day. (personaly i think that there is a finit amount of stars)

In mathematics, lets take a set of every positive numbers, let say that after x minutes you delete numbers ending by x-1 (the first minute you delete numbers ending with 0, the second minute you delete numbers ending with 1 etc). Each minute you delete 10 % of the original amount of numbers and after 10 minutes there is no more numbers.