2
votes
1answer
164 views

Can we embed the ordinal and cardinal number systems into larger, more convenient systems of arithmetic?

We can embed $\mathbb{N}$ in a larger number system, such as $\mathbb{Z}$, $\mathbb{Q}$ or $\mathbb{R}$, for convenience. Now since $\mathbb{N}$ is extended by $\mathrm{Ord}$ and $\mathrm{Card}$, the ...
1
vote
2answers
193 views

How big is the size of all infinities?

"Not only infinite - it's "so big" that there is no infinite set so large as the collection of all types of infinity..." What does exactly mean? How many infinities are there? I've heard there are ...
7
votes
3answers
859 views

The largest number system

If my number set construction memory doesn't fail me (I'll edit if errors are pointed out), we start out with Peano's axioms to get to $\mathbb{N}$, and in the need of an additive inverse for its ...