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Poster: People knew this 150 years ago
Subject: RE: If the universe is "expanding", how can it be infinite?
Body:

There are different sized infinities but this isn't an example. The set of irrationals in (0,1) is the same size as the set of irrationals in (0,100).

Both those sets are larger than the set of all integers. So you can't even "count" the irrationals in (0,1) or (0,100)--you run out of integers. The way we know the sets are the same size is by matching each element of one set with an element of the other set. The technical term for this is a bijective function (or simply a bijection).

In this particular case a bijection is f(x) = 100*x with inverse f^-1(x) = x/100. Thus the sets are the same size.

Todd from Texas wrote:

[quote]I think I got it wrote:

I'm pretty sure there are the same number of irrational numbers in the open intervals (0,1) and in (0,100).

The number of irrational numbers between 1 and 100 would have to be zero for your statement to be true.

Some infinites are bigger than others

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