Quote:
Originally Posted by Tubby
If the universe is infinite today' then yesterday it must have at least been somewhat less than infinite.
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In mathematical set theory that is wrong. You may go from one set with an infinite number of elements to another with an infinite numbers of elements, even if the first set is a true subset of the first.
There are infinite number of
natural (also called counting) numbers N
0 ),1,2,3,....
"Mathematicians use N or 
(an N in blackboard bold, displayed as ℕ
in Unicode) to refer to the set of all natural numbers. This set is countably infinite: it is infinite but countable by definition. This is also expressed by saying that the cardinal number of the set is aleph-nullhttp://en.wikipedia.org/wiki/Aleph_number#Aleph-null (
)".
My red colouring.
There are infinite number of rational numbers Q: n/m where n and m are positive or negative whole numbers.
There are infinite number of irrational numbers I like SQR(2).
There are infinite number of real numbers R = I U(nion) Q
Example:
N subset of Q that is a subset of R.
There are an over countalble number of elements in the Cantor set mentioned in the above post. That is the Cantor Set is
non countable.
You have to switch you brain to the mathematical part to understand this. Accept the building blocks, axioms and definitions. Doubt the definitions, and you may get a new (most probably inconsistent) theory.
The obeservable universe is 30 billion lightyears and that is definitely finite, though. So it may depend on the elements you are counting in your set or space.
Quote:
Originally Posted by Tubby
If the universe is infinite today' then yesterday it must have at least been somewhat less than infinite.
If you were to define a size for infinity. I could merely imagine it to be bigger and you would simply be wrong... such is the nature of a concept...
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So you did not read about cardinality above?