sykhi

Raymond just made up a religion for me. It was not meant by him to be serious. Our perceptions of reality appear to be very different.

It might be worth your time to consider the possibility that it is likely that the whole of the mathematics profession is not wrong in this matter. Are there any professional mathematicians that agree with you? If pretty much the whole profession thinks you are wrong about something then it’s quite likely you are indeed wrong.

It’s worth pointing out that your logic on Q = N times N is a bit faulty too. Since you are counting things like 4/4 as different than 1/1. Even so you are correct that the cardinality of Q is N times N. This is because N times N = N.

I met Raymond at a conference in the early 90s. I was an undergraduate in math then. We talked about philosophy, religion, and mathematics. Just the two of us. The next day he came up to me and said that he invented a religion for me.

God has a number in mind. If the sum total of good deeds minus bad deeds exceeds this number then everyone goes to heavan. If not then everyone goes to hell.

Then he said to me, “Imagine, something you do could send everyone to hell.”

Cardinality is the name given as a measure of the size of a set. The cardinality of the rationals is the same as the integers. The cardinality of the reals is larger than that of the integers.

There is an arithmetic of cardinal numbers and it is well understood if you accept the axiom of choice. For instance, using your notation, N*N = N and N^2 = N. You can read more here

https://en.m.wikipedia.org/wiki/Cardinal_number