I just learned something mindblowing: some infinities are bigger than others.
How can it be? Isn't infinity the maximum you can have? How come that not all infinities have the same size?
Let's start off easy, the number of counting numbers (1,2,3 up to infinity) is infinite; the number of irrational numbers (numbers that you cannot write as a fraction) is infinite. However, there are more irrational numbers than there are counting numbers; therefore, different orders of infinities. The number of "magic" numbers (π, e, etc) are apparently more numerous than the irrational numbers; therefore, an even bigger order of infinity.
*woah*
What about the infinity of the universe? Are there different orders of infinity there as well? Are there infinite while-loops of infinity with infinite while-loops inside of them?
Niel deGrasse Tyson in literally the first page of his book "Astrophysics for People in a Hurry" says: "The Universe is under no obligation of making sense to you". So it is normal if the fact that different sizes of infinities even exist might make you scratch your head.
That's all.
How can it be? Isn't infinity the maximum you can have? How come that not all infinities have the same size?
Let's start off easy, the number of counting numbers (1,2,3 up to infinity) is infinite; the number of irrational numbers (numbers that you cannot write as a fraction) is infinite. However, there are more irrational numbers than there are counting numbers; therefore, different orders of infinities. The number of "magic" numbers (π, e, etc) are apparently more numerous than the irrational numbers; therefore, an even bigger order of infinity.
*woah*
What about the infinity of the universe? Are there different orders of infinity there as well? Are there infinite while-loops of infinity with infinite while-loops inside of them?
Niel deGrasse Tyson in literally the first page of his book "Astrophysics for People in a Hurry" says: "The Universe is under no obligation of making sense to you". So it is normal if the fact that different sizes of infinities even exist might make you scratch your head.
That's all.
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