Here are 3 statements that I think are true but are not widely understood or accepted.

  1. There is no such thing as infinity in the real, physical world. The observable universe is not infinite, and nothing in it is infinite. Infinity is a mathematical abstraction, not a physical reality.

  2. Most of maths is incompatible with the concept of infinity. Most operations cannot be performed on infinities. Virtually every proof or operation in maths is so constructed as to avoid infinities. Where an infinity occurs, the maths fails.

  3. Infinity is given a specific meaning in maths, based on set theory, to allow it to be used in a certain restricted set of operations. It’s a very odd definition, and it takes some thinking about. The definition is (roughly):

    “An infinite set is one that can be placed in a one-to-one mapping with a subset of itself.”

    Only a mathematician could love it!