Here I found another huge problem with allowing several infinities and it's called the continuum hypothesis:

One expert said that Kurt Gödel proved in 1940 that CH can't be proved false. And then in 1963 Paul Cohen showed that CH can't be proved to be true! So CH can't be proven true or false. Sounds like inconsistency to me. To only allow one actual infinity will solve it since CH is then an invalid construction. And having only one actual infinity will cause a huge change in mathematics in many areas and not just for CH.

Quote:"In mathematics, the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite sets. It states:

There is no set whose cardinality is strictly between that of the integers and the real numbers." - Wikipedia

One expert said that Kurt Gödel proved in 1940 that CH can't be proved false. And then in 1963 Paul Cohen showed that CH can't be proved to be true! So CH can't be proven true or false. Sounds like inconsistency to me. To only allow one actual infinity will solve it since CH is then an invalid construction. And having only one actual infinity will cause a huge change in mathematics in many areas and not just for CH.