1. Contemplate on the word infinity. Think about what it represents. Now answer this question: do you think there are different sizes of infinity? Share your reasoning.
2. Give a 1- 2 sentence summary on Georg Cantor and his accomplishments.
3. Use your own words to define the terms "one-to-one", "rational", and "irrational".
4. Using the inequality symbol for less than (
Adrian Ward
homework goes in
Gabriel Bennett
OP here. I think infinity is infinite because that is just the way it is and why it exist. There are not multiple sizes of infinity just like there is only one GOD. Honestly, I'm not even sure if infinity exist. It could just be a made up concept. GOD on the other hand is not. I know for sure imaginary numbers are crap because they are imaginary. They wouldn't call them that otherwise. OP out. Just wanted some opinions.
Andrew Powell
That wasn't even funny. I'm not gay.
Gavin Myers
>1. Contemplate on the word infinity. Think about what it represents. Now answer this question: do you think there are different sizes of infinity? Share your reasoning.
Yes. Consider the size of a set and it's powerset. Through some reasoning, we can note that there can be no 1-1 and onto mapping from a collection of [math]n[/math] objects to a collection of [math]2^n[/math]. Therefore, there can be no mapping from an infinite set to it's collection of subsets.
2. Cantor proved that the rational numbers and the natural numbers have a bijective function, and that there cannot be a bijection between the natural numbers and the real numbers through two arguments.
3. 1-1, when describing a mapping f, means f(a)=f(b) implies a=b.
That's deep. I haven't watched the video yet but are those concepts presented in the video? Can a professor really expect a subpar pre-cal student to comprehend that?
Alexander Smith
No, just copy it, you'll totally be fine.
Yeah as far as I could tell that was entirely in the video.
Gavin Ward
Thanks. You are right. That stuff was in the video... mostly. To be honest, the video made me depressed and less interested in math.
Jayden Gomez
1. Muh "if it's true for all finite sets, then it's true for infinite sets." Is retarded. Hurrrr "all injections between finite sets are bijections, so therefore all injections between infinite sets are bijections" is a nice example of where that sort of logic fails.
2. There is a bijection between the naturals and the rationals, though :( They're both countably infinite :(
4.b. See 2. The cardinality is the same. Consider the mapping F(1)=1 F(2)=1/2 F(3)=1/3 F(4)=2/3 F(5)=1/4 F(6)=3/4 F(7)=1/5 Etc Covering all rational numbers.
Henry Mitchell
That user is simply wrong about a lot. Don't fucking copy it.
Jaxson Hernandez
I fucked up too, sorry. *covering all rationals between 0 and 1. It should be clear that this can be extended to all rationals though.
Xavier Collins
Its a lemniscate you fucking retards
Matthew Mitchell
>There is a bijection between the naturals and the rationals, though :( >They're both countably infinite :( That's what I said.
>The cardinality is the same. >Covering all rational numbers. The video uses decimals to mean reals.
You're probably correct about my powerset argument though.
Asher Cooper
1. I was being sarcastic about copying it.
2. You're a moron.
Connor Flores
That's the joy of being anonymous, you won't ever know who I am :^)
Do you have a problem with any of the math though? Aside from the fact that I completely misread that post.
Leo Cook
Nope, the mapping looks okay to me, so it's a solid post.
Austin Allen
Anything that is infinite is of infinite size. Therefore all infinite things are of equal size.
Thomas Cook
shut the fuck up. pretending to be retarded is really fucking retarded.
Hunter Cook
How is my claim retarded?
Chase Jenkins
Can someone explain to me in laymans terms Godel and Cohen proving that the continuum hypothesis can't be proven false or true? Do their proof's have anything to do with each other or are they independent? I wish the video went a little deeper into this, it's very fascinating.
