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Not all infinities are equal. Did you know some infinities are bigger than others?

When you think of infinity, you most likely think about Aleph Null infinity, aka countable infinity, aka the infinity "reached" by counting 1, 2, 3, 4, etc. An even bigger infinity is the number of real numbers between zero and one. This idea is a little hard to explain without diagrams, but one can essentially take any non-terminating decimal and change just one digit to create a brand new number. Irrational numbers are very neat, really. :D

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knel123

Wouldnt an infinity have infinite infinities in it?

TetrisGuy · 26-30, M

Infinity plus one is still infinity. Watch ViHart's video on infinity or look up the infinite hotel guests situation.

MalteseFalconPunch

There's countable infinities and then uncountable infinities. In a sense an uncountable set is "larger" than a countable one.

TetrisGuy · 26-30, M

Yup.

MalteseFalconPunch

Take the set of positive integers. It's countable because you can follow the sequence 1, 2, 3 etc... But the set of real numbers between 0 and 1 isn't countable. It's easier to understand if you start at 1 and head to 0. So start with 1 but what is the second term? 0.9? No, because 0.99 is in between 0.9 and 1. But 0.99 isn't right either because 0.999 is in between 0.99 and 1. And then 0.9999, 0.99999 etc... Since you can't even get to the second term in series that makes it "uncountable".

TetrisGuy · 26-30, M

You can be even simpler by saying that you'll never ever finish saying the first digit because you'll be like... point zero zero zero zero zero zero zero... *infinite time later* zero zero zero.... one. xD

When I was six or seven and didn't really understand the concept of the bar or know of the word "infinitesimal" I always said "point zero repeating one." xD

knel123

Alright. I was going to count infinity, but this has changed my mind. So ill just say infinity equals infinity and hope thats mathematical.

TetrisGuy · 26-30, M

Just take a Mobius Band, and write "1+1+1+1+1+1+" all around it to philosophically and somewhat mathematically capture the beauty of infinity.