What did I find difficult?
The concept of uncountable sets was difficult for me to understand at first. When I began reading the chapter, I thought I felt good about it all. I thought "you know, I understand what an infinity set is. When you have an open interval, you can get infinitely closer to the number at the end of the interval without ever reaching it. But, when I started getting to the proofs, things got more difficult for me. I understood that an open interval is infinite, but I was struggling with the proofs of it all.
I will need more experience with solving proofs, and will need to hear something think out loud when solving a proof showing that a set is uncountable. With that, I should be better at understanding this material.
What did I find interesting?
The whole idea of uncountable sets is fascinating. My whole life I've been dealing with finite sets, things I can wrap my head around. Now, things are getting a lot bigger a lot faster than I ever thought possible. It's exciting. Reading through the proofs are really cool. Proving that something is infinite is a way cool thing to think about. I just lack the faith that I can do it myself right now.
It's an interesting to think about - infinity. Something so big that it never ends. It keeps getting bigger and bigger and bigger or smaller and smaller and smaller. The other day, I let a balloon go, and it floated up and up and up and up. It got smaller and smaller and smaller. I stood riveted, watching it float away. I loved watching it. It got to the point where I feared blinking would prohibit me from finding it again. It kept getting smaller and smaller before it disappeared behind buildings. This is what infinitely smaller is for me. I'm excited to be able to prove that.
The concept of uncountable sets was difficult for me to understand at first. When I began reading the chapter, I thought I felt good about it all. I thought "you know, I understand what an infinity set is. When you have an open interval, you can get infinitely closer to the number at the end of the interval without ever reaching it. But, when I started getting to the proofs, things got more difficult for me. I understood that an open interval is infinite, but I was struggling with the proofs of it all.
I will need more experience with solving proofs, and will need to hear something think out loud when solving a proof showing that a set is uncountable. With that, I should be better at understanding this material.
What did I find interesting?
The whole idea of uncountable sets is fascinating. My whole life I've been dealing with finite sets, things I can wrap my head around. Now, things are getting a lot bigger a lot faster than I ever thought possible. It's exciting. Reading through the proofs are really cool. Proving that something is infinite is a way cool thing to think about. I just lack the faith that I can do it myself right now.
It's an interesting to think about - infinity. Something so big that it never ends. It keeps getting bigger and bigger and bigger or smaller and smaller and smaller. The other day, I let a balloon go, and it floated up and up and up and up. It got smaller and smaller and smaller. I stood riveted, watching it float away. I loved watching it. It got to the point where I feared blinking would prohibit me from finding it again. It kept getting smaller and smaller before it disappeared behind buildings. This is what infinitely smaller is for me. I'm excited to be able to prove that.
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