What about how there are infinite points on a line. Break a line in half: 1/2. Another half: 1/4. Then: 1/8, 1,16, 1/32, etc. The denominator amount has no limit. All of those intervals ACTUALLY EXIST on the line, so an infinite amount therefore exists in reality.
I have a rule of thumb that anything which says "infinity" is not actually mathematics. This is because there are a large number of mostly-unrelated concepts of the infinite in mathematics, and an actual mathematical usage would distinguish which one was being referred to.