Abstract
MR. BUDDEN'S paper in the last number of NATURE (p. 92) is full of inaccuracies of a more or less serious character. Without pointing out these, I wish to show that the essential idea which underlies his reasoning is altogether wrong, as it is based on the “infinite,” which he introduces in the most innocent manner by letting his figure grow without limit, and about which he then calmly reasons as if he still dealt with a finite figure. If we let a quantity “increase without limit,” we get a quantity which has increased beyond our comprehension, and no one in his senses will wittingly and seriously draw conclusions from what he does not comprehend. Here we might stop, were it not that the constant use in modern mathematics of the infinite (both the small and the great) has made us so familiar with it that an attempt to base an elementary proof on it might seem to many a very natural thing.
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HENRICI, O. Note on Mr. Budden's Proof that only One Parallel can be drawn from a Given Point to a Given Straight Line. Nature 35, 100 (1886). https://doi.org/10.1038/035100c0
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DOI: https://doi.org/10.1038/035100c0
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