| 1. | As Maelin says, it's a simple application of the pigeonhole principle.
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| 2. | Note that it is the pigeonhole principle that guarantees that a solution must exist.
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| 3. | It is an advanced generalization of the pigeonhole principle.
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| 4. | This is merely an instance of the pigeonhole principle.
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| 5. | For instance, the pigeonhole principle is of this form.
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| 6. | By operation of the pigeonhole principle, no lossless compression algorithm can efficiently compress all possible data.
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| 7. | :This is an instance of the Pigeonhole principle.
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| 8. | By the pigeonhole principle it will have a k-term monochromatic monotonic subsequence thereby finishing the problem.
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| 9. | In resolution or analytic Gentzen-style systems, the pigeonhole principle is known to have only exponential size proofs.
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| 10. | Then, by the pigeonhole principle, at least one line through " o " is the desired separator.
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