The Argument of Mathematics by Andrew Aberdein & Ian J Dove

Author:Andrew Aberdein & Ian J Dove
Language: eng
Format: epub
Publisher: Springer Netherlands, Dordrecht

11.6 Appendix: False Proofs

Three false proofs that were mentioned in this chapter appeared in Wikipedia (2007). Paraphrases of these false proofs are given below.

11.6.1 Proof that ∞ = 1 ∕ 4

To find the distance between, say − 4 and 3 (the points ( − 4, 0) and (3, 0) on the x-axis) one calculates , which gives 7. Generally, for points ( − a, 0) and (b, 0) the distance is equal to . The whole x-axis runs from − ∞ to ∞, its length is therefore equal to . The same is true for the y-axis. The area of the plane must be equal to the product of the lengths of the two axes, i.e. . Since the plane is infinite, we get: , which can be simplified into ∞ = (2∞)2. This yields to ∞ = 4∞ 2, from which we get , which simplifies into 1 = 4∞, and finally yields the value of the infinite: (this can be checked by substituting 1 ∕ 4 for ∞ in the equation , QED.

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