Random thoughts an random subjects

The article was made following a very productive afternoon nap. I sent this as an e-mail to a dear friend who I often discussed topics like this with and we still do it sometimes when drunk enough, alone enough or simply carried away enough.
I posted it here because if a thught is heard by someone else than it's maker it's only then it achieves it's true value.

You once told me that evolution is a fortunate series of events that lead to some more dominant and mutated specimens of a species to come up to existance and survive for loger and change. This was so unprobable that it took millions, even billions of years to happen, relying on the fact that if you give something sufficient time to happen it will happen eventually.

Now consider another thing:
There is such thing in mathematics called the cardinal number of the set of numbers (link: http://en.wikipedia.org/wiki/Cardinal_numbers). In short, it says that if you can make a bijective function between two sets of numbers (link: http://en.wikipedia.org/wiki/Bijective_function) those two sets of numbers will have the same cardinality or same cardinal number.
For instance, if you have x in {1,2,3} and y in {2, 3,4} you can make a simple bijection saying that y = x+1 and x = y-1. So, they have the same cardinal number 3.
There are some more examples on Wiki, look at them.

Now you look at continual functions, more precisly, probability. If you take any event that has two outcomes (will happen and won't happen) when you sum up their probabilities you get 1, flat. Let's say one probablility is x and the other is y, then they make x+y = 1.
Now, if both of probabilities are NOT zero (meaning they both CAN happen, as I said before) it means that they are numbers between 0 and 1. Let's say that x is greater or equal to y (it can be lower, in that case you turn the numbers around from this point on). That means you can find a number "k" that is higher than 1 and is finite (can be very big but not infinite) and make this:

y*k + y = y*(k+1) = 1, where x = y*k.

You can also write that:

y = 1/(k+1)

This function is a bijection because for the terms I stated above ( 0<1) for each y you can find a corresponding finite k and the other way around.
You can also do this for x the same way. This means that x and y and k all three have the same cardinal number because they are bijective. And if they have the same cardinal number that means the number of outcomes for the (near) infinite number of attempts the events will occur the same number of times at best (as crazy as it sounds but yes, think about it) or in short, they have the same set size.
On the other hand the probability says that the more times you repeat it the more the number of x and y events will be accurate to relation between x and y.

To conclude:
If y is a very rare event of a mutated species surviving for long enough to pass on its mutated genes and the event repeats itself for long enough by regular probability it would have happened with such a little probability that it is beyond comprehension. However, if you observe the cardinal number approach it says simply: it will have happend or it will have not, 50-50 chance.
If regular probability is right that means you, me and everyone surrounding us was SO lucky that we should be screaming of the billions of years of horror, constant expectation and hairline-close situations that preceede us.
If cardinal numbers are right it means that we have been lucky enought to have existed. It was either black or white
Whichever you choose to believe in you can say we were damn lucky. Or as Serbs preffer to say: Usralo nas.