Yeah, this is a good video but if you are getting lost then it's pointless because as the guy mentioned this stuff is learned by all math majors in day 1 of a proofs or real analysis class or both. So its audience must be non math majors.
There is a more satisfying way to prove that the real numbers are uncountable (in my opinion) by using the nested interval property, instead of using decimal expansions.
David Hilbert, one of the most important mathematicians of all time said "No one shall expel us from the paradise that Cantor has created" to give you some idea of how important these topics really are.
More interesting then all of this is the Cantor set, sometimes called Cantor dust. Wiki it and see if you can wrap your mind around that. It serves as a amazing example in analysis to challenge our understanding of the infinite.
1 comment:
Yeah, this is a good video but if you are getting lost then it's pointless because as the guy mentioned this stuff is learned by all math majors in day 1 of a proofs or real analysis class or both. So its audience must be non math majors.
There is a more satisfying way to prove that the real numbers are uncountable (in my opinion) by using the nested interval property, instead of using decimal expansions.
David Hilbert, one of the most important mathematicians of all time said "No one shall expel us from the paradise that Cantor has created" to give you some idea of how important these topics really are.
More interesting then all of this is the Cantor set, sometimes called Cantor dust. Wiki it and see if you can wrap your mind around that. It serves as a amazing example in analysis to challenge our understanding of the infinite.
Post a Comment