Sunday, March 11, 2012

10.3a, due March 12

Difficult: I don't understand when something is uncountable. I think I get when things are denumberable since I can find a bijective function with the natural numbers, but I have a hard time understanding when you can tell that something is uncountable without just thinking about it. Most of the theorems for this section i didn't understand at first, and sometimes even with the proof i didn't understand it, but then I would sit and think about it in relation to a denumberable set and then I could figure it out. Is there a different way to think about it though?

Reflective: I liked the part that talked about rational and irrational numbers being written as decimals. I think that this will help me with differentiating between rational and irrational numbers in the future because it is an additional way of thinking about it that I never really considered before. This also, in theory, helps with understanding the whole idea of something being uncountable.

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