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On the likelihood that life will originate given similar conditions (e.g. Earth-like planet) and due to the sheer number of habitable planets.
The whole thing hinges on whether the inverse of the probability of formation of a living thing is of similar order to the number of life-supporting planets.
The origin of life is both dependent on a supportive environment but due to its random origins dependent on a large amount of time.
Time is a continuous variable and if fragmented into ever smaller units can be compared to a real number line with time as the variable.
The size of a time set is of the same order as that of the size of the set of real numbers, which is uncountably infinite.
For each point in time, a unique set of events can be described in terms of specific atoms, each with a specific location or spatial co-ordinate.
There are of course other factors such as the velocity and direction of atoms and their relationship to each other, which would make the set even larger.
Simplistically, the sequence of events that originated in life on Earth can be designated by a set of atoms + coordinates for each point in time.
As this set is uncountably large, it cannot be matched to the size of the set of habitable planets even if this set is countably infinite.
Therefore, the conclusion that life must originate somewhere else in the universe is not supported in simple probabilistic terms.
However, if the universe has a "predisposition" to create life then the probability that life forms can only be measured in statistical terms by sampling.
At this point in time, there is no statistical evidence for life anywhere other than here on Earth.
Regards, Rob
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