Why did we even put infinity in math if it can't be solved?
You are pointing at a magical duality in maths, meaning some knowledge is hidden or missing in education. Since, the concept of infinity is foreign to the short-lived western civilization, the original definition for infinity is not concerned for unjustifiable pride; same with Atom (paramanu).
Following is how to get a logical feeling of infinity for mathematics, referencing to Prof. Lakshan Bandara's famous book "Through the Eyes of God of Gods - Unfinity and Unfinitesimal" .
The range of infinity:
starts after the boundary of finite and
ends before the boundary of everything/wholeness/completeness/universe.
Assume 1 to 100 is completeness.
If research scope is 1 to 60 in instance1, then 61 to 99 is the range of infinity.
If research scope is 1 to 75 in instance2, then 76 to 99 is the range of infinity.
Therefore, infinity in instance 2 is greater than infinity in instance1.
That is why the cardinality (number of elements) of natural numbers is twice the size of cardinality of natural even/odd numbers.
Further, refer to Georg Cantor's different types of infinity.
Any number divided by zero is undefinable, not infinity.
Completeness divided by infinitesimal is infinity.
Do not forget the 3 dimensional consideration in division.
These are fundamentals of Mathematics.