Once again, I see a proof in which the function is split up. In the proof of Theorem 10.19, it stated that s(sub n) = 1 if n in S and s(sub n) = 2 if n not in S. Also, it was stated that t(sub n) = 1 if n in T and t(sub n) = 2 if n not in T. I don't really understand, still, what this means. Why are they separated and equal to different numbers in different scenarios. My shallow understanding is to show that they have unique decimal expansions, but I'm not connecting the dots on how that shows it is unique. I should have probably asked a question in class a few weeks ago when a proof with a similar format was presented, but I didn't. Now I see it again and am still confused.
I find it kind of amusing that Cantor is left out of the Schroder-Bernstein Theorem. Poor Cantor! It is interesting who gets credit for what with scholarly discoveries. Will you be remembered forever for what you accomplished in your field or will your work be forgotten? While I'm fairly certain that I will not leave my mark in mathematics, it is inspiring to see these mathematicians excel in their field and be remembered and studied about by those that followed them. It inspires me to be the best I can be and to leave an impression on this world - even it is on a smaller scale, like with my children perhaps. That I can leave this world having benefited it or making it better for those who follow would be something to strive for.
No comments:
Post a Comment