Part 1

Proof that some infinities are bigger than other infinities

Proof that .999999… = 1

Proof that .999999… = 1 is wrong. I was confused about this since she proved this to be true in the earlier video, but then i realized that the video was posted on 4/1, and it was a joke.

Part 2

The first video talks about some infinities are bigger than other infinities The countable infinity are the integers you can count, 1 2 3 4 5 … The uncountable are numbers you can’t count, for example, all the real numbers between 0 and 1. This is much bigger than the countable infinity. No matter how close two numbers are, there will always be an infinite amount of real numbers between them. For example, what would the smallest real number bigger than 1? 1.0001, 1.0000001, 1.00000000001…? You would imagine that there would be a 1 somewhere at the end and infinity number of zeros in between. In fact, you just can’t list it because no matter what number you come up with, I can just add another zero in between and it would be smaller than your number. That’s why uncountable infinity is much bigger than the countable infinity.

Part 3

After watching the video, I was really amazed. I’ve learned a lot from it. I always thought that the biggest infinity would be infinite number of nines. I’ve never thought that there would be infinity between two numbers. Now I understand that it’s not the case. The uncountable infinity is much bigger than the countable infinity. Just the real numbers in between 0 and 1 is already larger than all the integers. When I become a teacher in the future, I can definitely teach my students about this.