Aleph naught (null) and Omega are said to be the “end of numbers” (cardinal or ordinal).
They are derived from the acceptance axioms - that is, if you resist the axions and insist on adding always a +1 since they do not have a natural, objective existence, don’t watch this video. But if you do, you’ll find this mind-blowing.
“The Outer Limits of Reason” by Noson S. Yanofsky: http://amzn.com/0262019353
“Infinity and The Mind” by Rudy Rucker: http://amzn.com/0691121273
“Roads to Infinity” by John C. Stilwell: http://amzn.com/1568814666
“More Precisely: The Math You Need to Do Philosophy” by Eric Steinhart: http://amzn.com/1551119099
“Satan, Cantor, and Infinity: Mind-Boggling Puzzles” by Raymond M. Smullyan: http://amzn.com/0486470369
a classic book that helps introduce the concept of axioms: “Introduction to the Foundations of Mathematics” by Raymond L. Wilder: http://amzn.com/0486488209
Hugh Woodin speaking about infinity at the World Science Festival: https://youtu.be/KDCJZ81PwVM?t=29m45s
Names of large (finite) numbers: https://en.wikipedia.org/wiki/Names_o...
The biggest number: https://goo.gl/maps/7GWcpnzo7iG2
and: https://en.wikipedia.org/wiki/Order_type and https://en.wikipedia.org/wiki/Well-order
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