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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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Tsunami3
Does this mean the infinity is "larger" or that it's just easier for us to grasp?
TetrisGuy · 26-30, M
It's larger.
Tsunami3
Sounds to me like an illusion caused by our inability to comprehend the extent of infinity, but I'm sure you'd call that incredulity :)
TetrisGuy · 26-30, M
It's not an illusion. It's been mathematically proven. That's the beauty of math.
Tsunami3
Has it? http://en.wikipedia.org/wiki/Controversy_over_Cantor's_theory
TetrisGuy · 26-30, M
That's not about the idea of infinity itself. That's the idea of the various types of infinity I describe here.