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There are multiple sets of infinite size. Lets take two: the set of all whole numbers (1,2,3,4...) and the set of even numbers (2,4,6,8...). Now since the set
by dazzawazza 14y ago
There are multiple sets of infinite size. Lets take two: the set of all whole numbers (1,2,3,4...) and the set of even numbers (2,4,6,8...).
Now since the set of whole numbers contains the set of even numbers AND the set of odd numbers the set of whole numbers MUST be bigger than the set of even numbers. So now we know that there are different 'sizes' of infinite (when comparing sets of infinite things).
This leads to the dangerous thought that there might be something MORE infinite than God which is an abomination. Since only god is infinite.
This kind of logic makes me cry.
- greenyoda 14y agoActually, the set of all whole numbers and the set of even numbers are the same size, since you can construct a one-to-one mapping between them: n -> 2n. Cantor famously showed that the set of rational numbers is the same size as the set of whole numbers. However, the set of real numbers can be proven to be larger than the set of integers.