I am less than an amateur mathematician. But I enjoy the Youtube channel numberphile so maybe I am slightly credible ? I have seen ∞ discussed in many forums, videos etc and many times there is always an idea of how infinity should not be thought of as a ‘number’. It’s a ‘concept’ as many would attempt to explain.
Then there is click-bait articles and videos that would tell you how one infinity might be bigger than another. And that is true. We can construct one ∞ that is larger than another ∞
So today, a mathematical brain fart occurred to me. Infinity is not a number nor it is a ‘concept’. I mean everything is a concept. But it is not merely a concept. I am proposing to look at ∞ as a unit of measurement.
And as every unit of measurement starts with an arbitrary ‘unit length’, I would like to define a unit of ∞ as the set of all natural numbers.
Once we have that, we can start to easily work with many other infinities. The set of even numbers thus is 1/2 of an ∞ (reading it now as 1 unit of measurement which equals the set of all natural numbers).
Larger infinities thus can also be worked out by using ∞ as 1 unit of measurement, being defined as I already mentioned.
Just a brain fart. But I wanted to publish this so that if there is something valuable in what I may have stumbled upon, I would love to have it attributed to me 😀