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!

Tessellations

Kazuma is helping me again. :) Tessellations are a pattern of shapes that fit perfectly together. Tessellations are classified as regular, semi-regular, and other tessellations. 

Regular tessellations are repetitions of 1 polygon. There are only three types of regular tessellations. Triangles, squares and hexagons. 

Semiregular tessellations are made of two or more regular polygons. There are 8 semi-regular polygons. For pictures click on this link. 

Other tessellations include demi-regular tessellations but mathematicians disagree on what defines them. 

Some authors define demi-regular polygons as orderly compositions of three regular and eight semi-regular tessellations. Other authors define demi-regular tessellations as a tessellation having more than 1 transitivity class of vertices.
Then, there are tessellations that have curved edges and circles.
Escher is a tessellation artist. He created pieces of art made with objects that can tessellate like the flying horses above. You can make your own tessellation with polygons at this tessellation maker.

 &

Proper Real Post #1

Ok, sorry for earlier, we had just created the site and we were feeling deliriously happy. So, anyway, I'm Strix Spell, I'm an administrator for this site. I will keep you posted on what goes on in the math world, complete with opinion on everything. I will be posting on Wednesdays, Saturdays and Sundays because Annis won't let me post every day.
Kazuma will be posting on Thursdays and Fridays. "He" will post some facts on math as well as a riddle on math at the end of each week.
Annis is posting on the new developments (without opinion) and the history of math on Mondays and Tuesdays.
Any questions? Ask away!

UPDATE: ok, I figured it out with the other admins and I'm posting about math, the two sides of the terms, why they are good and why they are bad.

Pi

Hi, I'm Kazuma. I'm in charge of the math facts.

Annis or Strix will cover for me if I forget. 

p.s... pi is 3.1415926535897 and so on...