Yes, you can call it "finitist" if you like but that is an error too. Define "exist".
Not "most" but all real numbers are similar to Pi, i.e. they are symbols that stand for an infinite process to calculate a rational number. Both irrational numbers like Pi, e, etc. and reals exists and are legit and useful math concepts but infinite precision does not exist "in the wild" only in your mind as an abstraction. In any actual calculation or measurement your infinite series must stop and the dedekind cut must be made.
The ghost of departed quantities still haunts math. Is Pi 3.14 or 3.1416? Mathematically, it is neither and both because math intentionally abstracts from the precision of the ratio of the circumference to the diameter of a circle. These open-ended (infinite) processes are ultimately used to define a rational number, a ratio of integers.The finitist -vs- infinitist is a false binary which ignore that actual measurement must use rational numbers.
Most natural numbers don't exist, for any useful definition of exist.
When you prove, say, by induction, that p(n) holds for any natural number n, and hear you teacher say that p(n) holds for all natural numbers, you start forming the idea that "all natural numbers" is a thing that exists. The set N, you think, surely by writing it, all natural numbers are called into existance.
And then, much later, you come upon problem, where actual existence of the number becomes better defined. Say, like finding a large prime. And suddenly "all numbers" becomes a confusing mental burden.
Not "most" but all real numbers are similar to Pi, i.e. they are symbols that stand for an infinite process to calculate a rational number. Both irrational numbers like Pi, e, etc. and reals exists and are legit and useful math concepts but infinite precision does not exist "in the wild" only in your mind as an abstraction. In any actual calculation or measurement your infinite series must stop and the dedekind cut must be made.
The ghost of departed quantities still haunts math. Is Pi 3.14 or 3.1416? Mathematically, it is neither and both because math intentionally abstracts from the precision of the ratio of the circumference to the diameter of a circle. These open-ended (infinite) processes are ultimately used to define a rational number, a ratio of integers.The finitist -vs- infinitist is a false binary which ignore that actual measurement must use rational numbers.