Infinity lets us have an easier time with certain things. Convergence is one example. When for example, let say we have an equation that is hard to solve. With infinity, we can have an infinite amount of terms that at the limit approximate that hard-to-solve equation. Even if it is not exactly the same thing, it is in some way good enough. If you took math in college, you might remember things like Taylor series or holomorphic / analytic functions. They all use the idea of infinity to achieve some sense of convergence.
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