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Continued from above.
Consider Euclidean and non-Euclidean geometry. The only difference between them is that the angles of a triangle either add up to exactly 180 degrees, or some number higher or lower than that. In each case, you can derive a whole universe full of conclusions about what the rest of that geometry will look like. So then, you observe the real world, and you check if angles total 180 or not. Recently, that was done where the triangle was composed of the earth, and 2 ends of a feature of the Cosmic Microwave Background (CMB). To a great deal of precision, the angles came to exactly 180 degrees. Then, everything we derive from Euclidean geometry that is mathematically rigorous will be true in the real world as well.
The same type of thing goes for going from an infinity in a mathematical expression to relating it to the real world.
Consider Euclidean and non-Euclidean geometry. The only difference between them is that the angles of a triangle either add up to exactly 180 degrees, or some number higher or lower than that. In each case, you can derive a whole universe full of conclusions about what the rest of that geometry will look like. So then, you observe the real world, and you check if angles total 180 or not. Recently, that was done where the triangle was composed of the earth, and 2 ends of a feature of the Cosmic Microwave Background (CMB). To a great deal of precision, the angles came to exactly 180 degrees. Then, everything we derive from Euclidean geometry that is mathematically rigorous will be true in the real world as well.
The same type of thing goes for going from an infinity in a mathematical expression to relating it to the real world.