Some Infinities are Bigger than Other Infinities

Hello, good day to you all!
I'm really sorry about not posting at all, I'm on vacation.
And now we're out of school, we can post more freely and you know, talk about our interests and discuss random things rather than focus on math.
So hello. It's Strix Spell here. I think Kazuma decided that she does not want to post anymore and Annis might, occasionally. I like to keep a schedule but well, that's near impossible now.
As well as talking about math, we can expand it to some more science as well.
Today, I'm focusing on the popular quote by John Green in his new book The Fault in Our Stars which I read and I'm going to review in my other blog.
Anyway, the quote is: "Some infinities are bigger than other infinities."
The thing about infinity, it is endless. It goes on and never stops, like a set of numbers (1,2,3,4...) So how are some infinities bigger than other infinities?
Hazel incorrectly explains it as: the set of numbers between 0 to 1 is a smaller infinity than the set of numbers between 0 and 2. While that is untrue, the statement some infinities are bigger than other infinities is still true.

That video explains a lot better than I can. But, if you are too lazy to watch the video, here is a random summary. While the set of numbers between 0 and 1 is the same number as the set of numbers between 0 and 2, we know that the set of numbers between 0 and 1 is bigger than the set of positive integers (1,2,3,4...). 

Okay, I can't explain so haha! You have to watch the video to understand. 

Anyway, basically, what I am trying to point out is that some infinities are bigger than other infinities. Yay!

Goodbye Answers

The answer key, also known as Tricky and Twisted Math has been reverted to draft because Kazuma, Annis, and I are doing a class thing and we need the students to figure it out on their own rather than cheat so, sorry!

Problem of the Day #10

Hooray, we are on 10!
So, more patterns, oh, and this has something to do with twin primes.

What comes next in this sequence? 4, 6, 12, 18, 30, 42, 60, 72, 102, 108,...?
Have fun solving!

Problem of the Day #9

Sorry for not posting yesterday.
There were some complications but, I'm here today!
I like patterns so here is another riddle for patterns.
1 = 3, 2 = 3, 3 = 5, 4 = 4, 5 = 4, 6 = 3, 7 = 5, 8 = 5, 9 = 4, 10 = 3, 11 = ?, 12 = ?
What do eleven and twelve equal?

The rest of the alphabet!

Yay! More alphabet! Nu is up and its main importance in math is that it represents the degrees of freedom! The degrees of freedom is the number of values in the final calculation of a statistic that are free to vary. Xi is frequently used in statistics as well. The xi squared distribution is a theoretical probability distribution used in inferential statistics. χ2 = ∑( Oi - Ei)² / Ei  is the value of  the xi squared distribution. For omicron, the capital O in omicron is for the big O notation that describes limiting behavior of a function when the argument tends toward a particular value or infinity, usually in terms of smaller functions. Pi is of course pi. Pi is the ratio of a circle's circumference to its diameter, or 3.14159265358979323846264... For rho, there is the analytic number theory invented by Leopold Gegenbauer. The following is the analytic number theory.

Sigma is probably the most significant and used alphabet letter in math and science. Anyway, sigma is the summation operator. Summation is the operation of adding a sequence of numbers; the result is their sum/total. For tau, ther was a bunch of uses, but I chose a function because functions are fun! I don't exactly know what is describes but here it is!

For upsilon, all I found was the elementary particle, but no one seems to know what it is. Now, for phi! It's the golden ratio! You probably know about this from Strix's post but the Golden Ratio is 1.618... The golden ratio is a number encountered when taking the ratios of distances into simple geometric figures.

Now for chi! Guess what?! The Euler characteristic is denoted as X, because we know V+F-E will not always be two...  For psi, it's the reciprocal of the Fibonacci numbers! You might know the Fibonaccis from Strix's post, This time it's just 1/1(the first number) + 1/the second number + 1/the third number +...  Lastly, the omega constant! It's really just a constant defined by omega times e to the power of omega= 1. Yay! We are done! See Ya!