06:33 pm - Careful with your infinities.
Fundie proof of God.
The crux of this argument is that there cannot have been an infinite amount of time in the past, because you cannot count from infinitely far back up to now, therefore if there was an infinite amount of time in the past, we would never have reached the present.
Setting aside current scientific theories about time being a function of perception, here's a little mathematical proof of something.
Let two numbers a, b ∈ Q (the set of rational numbers) such that a < b.
The definition of a rational number is that it can be expressed as v/w where v, w ∈ Z and w≠0.
Therefore, let c, d, e, f ∈ Z such that c/d = a and e/f = b.
Find g, h ∈ Z such that gd = hf.
Let i = gd = hf. i ∈ Z because g, d, h, f ∈ Z.
Thus c/d = gc/i and e/f = he/i.
A new number j that is halfway between a and b is therefore ((gc + he)/2)/i.
This simplifies to (gc + he)/2i.
Because g, c, h, e ∈ Z, (gc + he) ∈ Z. Because i ∈ Z, 2i ∈ Z.
Therefore, a < j < b, and j ∈ Q.
Because a and b were arbitrary, we can use universal generalisation to get: ∀x∈Q∀y∈Q(x<y→∃z∈Q(x<z∧z<y)).
What does this prove? It proves that the set of all rational numbers is dense, meaning that no matter what two rational numbers you choose (as long as they are not equal), you can find another rational number between them. This, by extension, means there are an infinite number of rational numbers in any given range. If it's impossible to get to this time from a time infinitely far in the past, then it's also impossible to count from 2 to 3, because there are an infinite number of rational numbers in between them. Just for fun, let's prove that it is possible to count from two to three, by mathematical induction.
Base case
i0=2.
Inductive step
in=in-1+1.
Therefore i1=3. Whoa, that was easy.
I do imagine that most people who see this won't understand it. That's okay, all I really wanted to say is: beware of any argument that relies on infinity.
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